# Trigonometry & Complex Numbers

## Video Lectures

Displaying all 168 video lectures.
I. Angles and Arc Length
Lecture 1

Play Video
Finding the Quadrant in Which an Angle Lies - Example 1
Finding the Quadrant in Which an Angle Lies - Example 1. In this video, I consider a few different angle (measured in degrees) and find the quadrant which they would belong to.
Lecture 2

Play Video
Finding the Quadrant in Which an Angle Lies - Example 2
Finding the Quadrant in Which an Angle Lies - Example 2. In this video, I consider a few different angle (measured in degrees) and find the quadrant which they would belong to.
Lecture 3

Play Video
Finding the Quadrant in Which an Angle Lies - Example 3
Finding the Quadrant in Which an Angle Lies - Example 3. In this video, I consider a few different angle (measured in degrees) and find the quadrant which they would belong to.
Lecture 4

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Coterminal Angles - Example 1
Coterminal Angles - Example 1. In this video, I discuss what it means for two angles to be coterminal, and discuss a quick method on how to decide if two angles are in fact coterminal. Then I do a couple of examples of finding angles that are coterminal to each other.
Lecture 5

Play Video
Coterminal Angles - Example 2
Coterminal Angles - Example 2. Just more questions about deciding if angles are coterminal or not!
Lecture 6

Play Video
Complementary and Supplementary Angles - Example 1
Complementary and Supplementary Angles - Example 1. In this video, I discuss what it means for angles to be complementary and supplementary and do a few problems where I find complements and supplements for different angles.
Lecture 7

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Complementary and Supplementary Angles - Example 2
Complementary and Supplementary Angles - Example 2. In this video, I create a system of linear equations to find the measure of an angle knowing information about its complement and supplement.
Lecture 8

Play Video
Degrees and Radians and Converting Between Them! Example 1
Degrees and Radians and Converting Between Them! Example 1. In this video, I discuss how to go from degree measure to radian measure.
Lecture 9

Play Video
Arc Length Formula - Example 1
Arc Length Formula - Example 1. In this video, I discuss the formula for arc length and use it in a couple of examples.
Lecture 10

Play Video
Arc Length Formula - Example 2
Arc Length Formula - Example 2. In this video, I use the arc length formula to estimate the height of a tree.
II. Trigonometric Functions
Lecture 11

Play Video
Finding Trigonometric Function Values Given One Trig Value in a Right Triangle, Ex 1
Finding Trigonometric Function Values Given One Trig Value in a Right Triangle, Ex 1. In this video, I give the value of one of the trigonometric functions and I deduce all of the other ones.
Lecture 12

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Finding Trigonometric Function Values Given One Trig Value in a Right Triangle, Ex 2
Finding Trigonometric Function Values Given One Trig Value in a Right Triangle, Ex 2. In this video, I do a word problem to find the area of a triangle that is attached to a square. We know the area of the square (it is given) and we know a value for tangent for one angle of the triangle; we use this info to find the area of the triangle.
Lecture 13

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Finding Trigonometric Function Values Given One Trig Value in a Right Triangle, Ex 3
Finding Trigonometric Function Values Given One Trig Value in a Right Triangle, Ex 3. In this video, we first use the Pythagorean Theorem to find the missing value for one side of a right triangle; from there we simply use the definition of cotangent to find the cotangent of one of the given angles in the triangle.
Lecture 14

Play Video
Finding an Angle Given the Value of a Trigonometric Function - Example 1
Finding an Angle Given the Value of a Trigonometric Function - Example 1. In this video, I deduce the angle associated with a given trigonometric value.
Lecture 15

Play Video
Finding an Angle Given the Value of a Trigonometric Function - Example 2
Finding an Angle Given the Value of a Trigonometric Function - Example 2. In this video, I deduce the angle associated with a given trigonometric value.
Lecture 16

Play Video
Trigonometric Functions To Find Unknown Sides of Right Triangles, Ex 1
Trigonometric Functions To Find Unknown Sides of Right Triangles, Ex 1. In this video, I use information about the length of the hypotenuse of a right triangle as well as a trig value to find the area of the triangle.
Lecture 17

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Trigonometric Functions To Find Unknown Sides of Right Triangles, Ex 2
Trigonometric Functions To Find Unknown Sides of Right Triangles, Ex 2. In this video, I use information about the length of the hypotenuse of a right triangle as well as a trig function to find the length of a missing side.
Lecture 18

Play Video
Trigonometric Functions To Find Unknown Sides of Right Triangles, Ex 3
Trigonometric Functions To Find Unknown Sides of Right Triangles, Ex 3. In this video, I use information about the length of the hypotenuse of a right triangle as well as a trig function to find the length of a missing side.
Lecture 19

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Finding the Height of an Object Using Trigonometry, Example 1
Finding the Height of an Object Using Trigonometry, Example 1. In this video, I find the height of a balloon by knowing a horizontal distance and an angle.
Lecture 20

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Finding the Height of an Object Using Trigonometry, Example 2
Finding the Height of an Object Using Trigonometry, Example 2. In this video, I find the height of a balloon by knowing a horizontal distance and an angle.
Lecture 21

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Finding the Height of an Object Using Trigonometry, Example 3
Finding the Height of an Object Using Trigonometry, Example 3. In this video, I find the height of a balloon by knowing a horizontal distance and an angle.
Lecture 22

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Lecture 23

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A Way to remember the Entire Unit Circle for Trigonometry
Where Do These Values Come From? https://www.youtube.com/watch?v=3GgO7Q_kg8Q
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Trigonometry Review Questions With Solutions Made by Me! http://www.teacherspayteachers.com/Product/Trigonometry-Revi...
How to Derive the Values on the Unit Circle http://www.youtube.com/watch?v=3GgO7Q_kg8Q
Closed Captioning Available for this video.
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A way to remember the Entire Unit Circle for Trigonometry. This is the way that I remember the unit circle.
Lecture 24

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A Trick to Remember Values on The Unit Circle
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A Trick to Remember Values on The Unit Circle - People often forget what x,y coordinates on the unit circle go with what angle. In this video, I show a little 'trick' to remember the values on the unit circle in the first quadrant.

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Lecture 25

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Evaluating Trigonometric Functions for an Unknown Angle, Given a Point on the Angle, Ex 1
Evaluating Trigonometric Functions for an Unknown Angle, Given a Point on the Angle, Ex 1. In this video, I give a point that falls on the terminal side of an angle, and use that to evaluate the trig functions at that angle.
Lecture 26

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Evaluating Trigonometric Functions for an Unknown Angle, Given a Point on the Angle, Ex 2
Evaluating Trigonometric Functions for an Unknown Angle, Given a Point on the Angle, Ex 2. In this video, I give a point that falls on the terminal side of an angle, and use that to evaluate the trig functions at that angle.
Lecture 27

Play Video
Reference Angle for an Angle, Ex 1 (Using Degrees)
Reference Angle for an Angle, Ex 1 (Using Degrees). In this video, I find the reference angle for a few angles that are measured in degrees.
Lecture 28

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Reference Angle for an Angle, Ex 2 (Using Radians)
Reference Angle for an Angle, Ex 1 (Using Radians). In this video, I find the reference angle for a few angles that are measured in degrees.
Lecture 29

Play Video
Evaluating Trigonometric Functions Using the Reference Angle, Example 1
Evaluating Trigonometric Functions Using the Reference Angle, Example 1. In this video, I do a quick review of the unit circle in quadrant 1 and discuss how to use the reference angle to evaluate some trig functions.
Lecture 30

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Evaluating Trigonometric Functions Using the Reference Angle, Example 2
Evaluating Trigonometric Functions Using the Reference Angle, Example 2. In this video, I discuss how to use the reference angle to evaluate some more trig functions.
Lecture 31

Play Video
Finding Trigonometric Values Given One Trigonometric Value/Other Info, Example 1
Finding Trigonometric Values Given One Trigonometric Value/Other Info, Example 1. In this video, I give the value of sin(x) and cos(x) and use that to find the values of the other trig functions.
Lecture 32

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Finding Trigonometric Values Given One Trigonometric Value/Other Info, Example 2
Finding Trigonometric Values Given One Trigonometric Value/Other Info, Example 2. In this video, we are given the value of one trig function along with the quadrant where the angle belongs, and use it to find the value of the other trig functions.
Lecture 33

Play Video
Evaluating Trigonometric Functions at Important Angles, Ex 1
Evaluating Trigonometric Functions at Important Angles, Ex 1. In this video, I show how to use the unit circle and reference angles to find some values for different trig functions.
Lecture 34

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Evaluating Trigonometric Functions at Important Angles, Ex 2
Evaluating Trigonometric Functions at Important Angles, Ex 2. In this video, I show how to use the unit circle and reference angles to find some values for different trig functions.
III. Graphing Trigonometric Functions
Lecture 35

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The Graph of Cosine, y = cos (x)
The Graph of Cosine, y = cos (x). This is the way I think about it and graph it! I simply think about the unit circle, the definition of cosine and plot points.
Lecture 36

Play Video
Graphing Sine and Cosine With Different Coefficients (Amplitude and Period), Ex 1
Graphing Sine and Cosine With Different Coefficients, Ex 1. In this video, I talk about how to find the amplitude and period of a couple of functions. In the second example, I actually sketch a concrete example.
Lecture 37

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Graphing y = -2 cos(2x)
Lecture 38

Play Video
Maximum and Minimum Values of Sine and Cosine Functions, Ex 1
Maximum and Minimum Values of Sine and Cosine Functions, Ex 1. In this video, I talk about how to find the maximum and minimum values of sine and cosine functions with different coefficients thrown in!
Lecture 39

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Maximum and Minimum Values of Sine and Cosine Functions, Ex 2
Maximum and Minimum Values of Sine and Cosine Functions, Ex 2. In this video, I do a 'word problem' andI talk about how to find the maximum value of a cosine function.
Lecture 40

Play Video
Graphing Sine and Cosine with Phase (Horizontal) Shifts, Example 1
In this video, I show how to find the phase shift (aka, the horizontal shift) of a couple of trig functions. In the next video, I actually graph a trig function by thinking about phase shifts.
Lecture 41

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Graphing Sine and Cosine with Phase (Horizontal) Shifts, Example 2
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In this video, I graph a trigonometric function by graphing the original and then applying the phase shift.
Lecture 42

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Trigonometric Functions and Graphing: Amplitude, Period, Vertical and Horizontal Shifts, Ex 2
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Trigonometric Functions and Graphing: Amplitude, Period, Vertical and Horizontal Shifts, Ex 2. In this video, I find the amplitude, period, vertical and horizontal shifts for a trig function and use that to graph the function.
Lecture 43

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Basic Questions Related to Tangent, Cotangent, Secant, Cosecant, Ex 1
Basic Questions Related to Tangent, Cotangent, Secant, Cosecant, Ex 1. In this video, I just address a few basic questions about Tangent, Cotangent, Secant, Cosecant.
Lecture 44

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Basic Questions Related to Tangent, Cotangent, Secant, Cosecant, Ex 2
Basic Questions Related to Tangent, Cotangent, Secant, Cosecant, Ex 2. In this video, I just address a few basic questions about Tangent, Cotangent, Secant, Cosecant.
Lecture 45

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Basic Questions Related to Tangent, Cotangent, Secant, Cosecant, Ex 4
Basic Questions Related to Tangent, Cotangent, Secant, Cosecant, Ex 4.
Lecture 46

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Finding a Formula for a Trigonometric Graph, Ex 1
Finding a Formula for a Trigonometric Graph, Ex 1. In this video, we are given a graph of a trigonometric functions and we have to find the formula to best describe it.
Lecture 47

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Finding a Formula for a Trigonometric Graph, Ex 2
Finding a Formula for a Trigonometric Graph, Ex 2. In this video, we are given a graph of a trigonometric functions and we have to find the formula to best describe it.
Lecture 48

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Trigonometry Word Problem, Finding The Height of a Building, Example 1
Trigonometry Word Problem, Finding The Height of a Building, Example 1. In this video, I use a bit of trigonometry to find the height of a building.
Lecture 49

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Trigonometry Word Problem, Example 2
Trigonometry Word Problem, Example 2. In this video, I use a bit of trigonometry to find the elevation gain of a hiker going up a slope.
Lecture 50

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Trigonometry Word Problem, Determining the Speed of a Boat, Example 3
Trigonometry Word Problem, Determining the Speed of a Boat, Example 3. In this video, I use a bit of trigonometry to find the speed of a moving boat.
IV. Simplifying Trigonometric Expressions
Lecture 51

Play Video
Simplifying Trigonometric Expressions Using Identities, Example 1
Simplifying Trigonometric Expressions Using Identities, Example 1. In this video, I simplify a trigonometry expression using some trig identities.
Lecture 52

Play Video
Simplifying Trigonometric Expressions Using Identities, Example 2
Simplifying Trigonometric Expressions Using Identities, Example 2. In this video, I simplify a trigonometry expression using some trig identities.
Lecture 53

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Simplifying Trigonometric Expressions Using Identities, Example 3
Simplifying Trigonometric Expressions Using Identities, Example 3. In this video, I simplify a trigonometry expression using some trig identities.
Lecture 54

Play Video
Simplifying Trigonometric Expressions Involving Fractions, Ex 1
Simplifying Trigonometric Expressions Involving Fractions, Ex 1
Lecture 55

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Simplifying Trigonometric Expressions Involving Fractions, Example 2
Simplifying Trigonometric Expressions Involving Fractions, Example 2
Lecture 56

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Simplifying Products of Binomials Involving Trigonometric Functions, Ex 1
Simplifying Products of Binomials Involving Trigonometric Functions, Ex 1
Lecture 57

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Simplifying Products of Binomials Involving Trigonometric Functions, Ex 2
Simplifying Products of Binomials Involving Trigonometric Functions, Ex 2
Lecture 58

Play Video
Factoring Trigonometric Expressions, Example 1
Factoring Trigonometric Expressions, Example 1
Lecture 59

Play Video
Factoring and Simplifying Trigonometric Expressions - Example 2
Factoring and Simplifying Trigonometric Expressions - Example 2
V. Even and Odd Functions
Lecture 60

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Examples with Trigonometric Functions: Even, Odd or Neither, Example 1
Examples with Trigonometric Functions: Even, Odd or Neither, Example 1
Lecture 61

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Examples with Trigonometric Functions: Even, Odd or Neither, Example 2
Examples with Trigonometric Functions: Even, Odd or Neither, Example 2
Lecture 62

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Examples with Trigonometric Functions: Even, Odd or Neither, Example 3
Examples with Trigonometric Functions: Even, Odd or Neither, Example 3
Lecture 63

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Even, Odd or Neither, Trigonometric Functions, Example 4
Even, Odd or Neither, Trigonometric Functions, Example 4
Lecture 64

Play Video
Proving an Identity, Example 1
Proving an Identity, Example 1
Lecture 65

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Proving an Identity, Example 2
Proving an Identity, Example 2
Lecture 66

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Proving an Identity - Other Examples, Example 1
Proving an Identity - Other Examples, Example 1
Lecture 67

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Proving an Identity - Other Examples, Example 2
Proving an Identity - Other Examples, Example 2
Lecture 68

Play Video
Solving a Basic Trigonometric Equation, Example 1
Solving a Basic Trigonometric Equation, Example 1
Lecture 69

Play Video
Solving a Basic Trigonometric Equation, Example 2
Solving a Basic Trigonometric Equation, Example 2
Lecture 70

Play Video
Solving a Basic Trigonometric Equation, Example 3
Solving a Basic Trigonometric Equation, Example 3
Lecture 71

Play Video
Solve Trigonometric Equation by Factoring, Example 1
Solving a Trigonometric Equation by Factoring, Example 1
Lecture 72

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Solving a Trigonometric Equation by Factoring, Example 2
Solving a Trigonometric Equation by Factoring, Example 2
Lecture 73

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Solving a Trigonometric Equation by Factoring, Example 3
Solving a Trigonometric Equation by Factoring, Example 3
Lecture 74

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Solving Trigonometric Equation, Harder Example - Example 1
Solving Trigonometric Equations with Coefficients in the Argument - Example 1
Lecture 75

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Solving Trigonometric Equation, Harder Example - Example 2
Solving Trigonometric Equations with Coefficients in the Argument - Example 2
Lecture 76

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Solving Trigonometric Equation , Harder Exampe - Example 3
Solving Trigonometric Equations with Coefficients in the Argument - Example 3
Lecture 77

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Solving Trigonometric Equations Using the Quadratic Formula - Example 1
Solving Trigonometric Equations Using the Quadratic Formula - Example 1
Lecture 78

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Solving Trigonometric Equations Using the Quadratic Formula - Example 2
Solving Trigonometric Equations Using the Quadratic Formula - Example 2
Lecture 79

Play Video
Solving Trigonometric Equations Using the Quadratic Formula - Example 3
Solving Trigonometric Equations Using the Quadratic Formula - Example 3
Lecture 80

Play Video
Solving Word Problems Involving Trigonometric Equations, Example 1
Solving Word Problems Involving Trigonometric Equations, Example 1. In this video I look at the equations describing the motion of a particular spring and answer some questions about it! For more free math videos, visit http://PatrickJMT.com
Lecture 81

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Solving Word Problems Involving Trigonometric Equations, Example 2
Solving Word Problems Involving Trigonometric Equations, Example 2. For more free math videos, visit http://PatrickJMT.com
VI. Sum and Difference Trig Identities
Lecture 82

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Identities for Sum and Differences of Sine and Cosine, Example 1
Identities for Sum and Differences of Sine and Cosine, Example 1. In this video, I show how we can find other values of sine and cosine (besides the commonly memorized values) using sum and difference identities. For more free math videos, visit http://PatrickJMT.com
Lecture 83

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Identities for Sum and Differences of Sine and Cosine, Example 2
Identities for Sum and Differences of Sine and Cosine, Example 2. In this video, I show how we can find other values of sine and cosine (besides the commonly memorized values) using sum and difference identities. For more free math videos, visit http://PatrickJMT.com
Lecture 84

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Identities for Sum and Differences of Sine and Cosine, Example 3
Identities for Sum and Differences of Sine and Cosine, Example 3. In this video, I show how we can find other values of tangent (besides the commonly memorized values) using sum and difference identities. For more free math videos, visit http://PatrickJMT.com (Yes, there is a formula for tangent as well, but here I wanted to stress the sine/cosine formulas!)
Lecture 85

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Sum and Difference Identities for Sine and Cosine, More Examples #1
Sum and Difference Identities for Sine and Cosine, More Examples #1. More examples of using the sum and difference identities to find value other trig values. For more free math videos, visit http://PatrickJMT.com
Lecture 86

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Sum and Difference Identities for Sine and Cosine, More Examples #2
Sum and Difference Identities for Sine and Cosine, More Examples #2. More examples of using the sum and difference identities to find value other trig values. For more free math videos, visit http://PatrickJMT.com
Lecture 87

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Sum and Difference Identities for Sine and Cosine, More Examples #3
I SAY COS(X) IS NEGATIVE IN Q4, BUT IT SHOULD BE POSITIVE! SORRY FOR THE CONFUSION!
Sum and Difference Identities for Sine and Cosine, More Examples #3. More examples of using the sum and difference identities to find value other trig values. For more free math videos, visit http://PatrickJMT.com
Lecture 88

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Sum and Difference Identities to Simplify an Expression, Example 1
Sum and Difference Identities to Simplify an Expression, Example 1. In this video, I simply show how to simplify some expressions by using sum and difference identities. Nothing crazy, just showing how one must know identities to make things more manageable! For more free math videos, visit http://PatrickJMT.com
Lecture 89

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Sum and Difference Identities to Simplify an Expression, Example 2
Sum and Difference Identities to Simplify an Expression, Example 2. In this video, I simply show how to simplify some expressions by using sum and difference identities. Nothing crazy, just showing how one must know identities to make things more manageable! For more free math videos, visit http://PatrickJMT.com
Lecture 90

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Sum and Difference Identities to Simplify an Expression, Example 3
Sum and Difference Identities to Simplify an Expression, Example 3. In this video, I simply show how to simplify some expressions by using sum and difference identities. Nothing crazy, just showing how one must know identities to make things more manageable! For more free math videos, visit http://PatrickJMT.com
Lecture 91

Play Video
Using the Sum and Difference Identities for Sine, Cosine and Tangent, Ex 1
Using the Sum and Difference Identities for Sine, Cosine and Tangent, Ex 1. Just a few examples using the sum and difference identities for sine, cosine and tangent. For more free videos, visit http://PatrickJMT.com
Lecture 92

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Using the Sum and Difference Identities for Sine, Cosine and Tangent, Ex 2
Using the Sum and Difference Identities for Sine, Cosine and Tangent, Ex 2. Just a few examples using the sum and difference identities for sine, cosine and tangent. For more free videos, visit http://PatrickJMT.com
Lecture 93

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Using the Sum and Difference Identities for Sine, Cosine and Tangent, Ex 3
Using the Sum and Difference Identities for Sine, Cosine and Tangent, Ex 2. Just a few examples using the sum and difference identities for sine, cosine and tangent. For more free videos, visit http://PatrickJMT.com
VII. Double Angle Trig Identities
Lecture 94

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Using Double Angle Identities to Solve Equations, Example 1
Using Double Angle Identities to Solve Equations, Example 1.
In this video, I use some double angle identities for sine and/or cosine to solve some equations. Great fun!! For more free math videos, visit http://PatrickJMT.com
Lecture 95

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Using Double Angle Identities to Solve Equations, Example 2
Using Double Angle Identities to Solve Equations, Example 2.
In this video, I use some double angle identities for sine and/or cosine to solve some equations. Great fun!! For more free math videos, visit http://PatrickJMT.com
Lecture 96

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Using Double Angle Identities to Solve Equations, Example 3
Using Double Angle Identities to Solve Equations, Example 3.
In this video, I use some double angle identities for sine and/or cosine to solve some equations. Great fun!! For more free math videos, visit http://PatrickJMT.com
Lecture 97

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Word Problems Involving Multiple Angle Identities, Example 1
Word Problems Involving Multiple Angle Identities, Example 1. Just some random word problems that make use of the double angle formulas (as well as others!).
Lecture 98

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Word Problems Involving Multiple Angle Identities, Example 2
Word Problems Involving Multiple Angle Identities, Example 2. Just some random word problems that make use of the double angle formulas (as well as others!
Lecture 99

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Word Problems Involving Multiple Angle Identities, Example 3
Word Problems Involving Multiple Angle Identities, Example 3. Just some random word problems making use of the double angle identities (and others!).
Lecture 100

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Cofunction Identities, Example 2
Cofunction Identities, Example 2. In this video I use a cofunction identity to simplify an expression.
Lecture 101

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Cofunction Identities, Example 3
Cofunction Identities, Example 3. In this video I use a cofunction identity to simplify an expression.
Lecture 102

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Power Reducing Formulas for Sine and Cosine, Example 1
Power Reducing Formulas for Sine and Cosine, Example 1. In this video, I give a formula for (sinx)^2 and (cosx)^2 in terms of cosx.
Lecture 103

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Power Reducing Formulas for Sine and Cosine, Example 2
Power Reducing Formulas for Sine and Cosine, Example 2. In this video, I give a formula for (sinx)^2 and (cosx)^2 in terms of cosx.
Lecture 104

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Half Angle Identities to Evaluate Trigonometric Expressions, Example 1
Half Angle Identities to Evaluate Trigonometric Expressions, Example 1. In this video, I give some half angle identities and show how they can be used to solve some trigonometric equations.
Lecture 105

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Half Angle Identities to Evaluate Trigonometric Expressions, Example 2
Half Angle Identities to Evaluate Trigonometric Expressions, Example 2. In this video, I give some half angle identities and show how they can be used to evaluate trigonometric expressions.
Lecture 106

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Half Angle Identities to Evaluate Trigonometric Expressions, Example 3
Half Angle Identities to Evaluate Trigonometric Expressions, Example 3. In this video, I give some half angle identities and show how they can be used to evaluate trigonometric expressions.
VIII. Law of Sines
Lecture 107

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The Law of Sines, Example 1
The Law of Sines, Example 1.
This video talks a bit about the Law of Sines. I give the formula and proceed to do an example using it. Very exciting!! (it actually is quite useful though)
Lecture 108

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The Law of Sines, Example 2
The Law of Sines, Example 2.
This video talks a bit about the Law of Sines. I give the formula and proceed to do an example using it.
Lecture 109

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Law of Sines, Example 3
The Law of Sines, Example 3.
In this video, I just another example involving the law of sines. We are given the ratio of the lengths of the angles of the triangle and the length of the shortest side and are asked to find the length of the longest side.
Lecture 110

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Side Angle Side for Triangles, Finding Missing Sides/Angles, Example 1
Side Angle Side for Triangles, Finding Missing Sides/Angles, Example 1. In this video, we determine some missing angles and side lengths for a given triangle.
Lecture 111

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Side Angle Side for Triangles, Finding Missing Sides/Angles, Example 2
Side Angle Side for Triangles, Finding Missing Sides/Angles, Example 2. Here we make use of the law of sines to find a missing angle value.
Lecture 112

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Solving a Triangle, SSA, Example 1
Solving a Triangle, SSA, Example 1. In this video, we find a missing side length using SSA and the law of sines.
Lecture 113

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Solving a Triangle, SSA, Example 2
Solving a Triangle, SSA, Example 2. In this video, we find some missing angle values using SAS and the law of sines.
Lecture 114

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Law of Sines - Application/Word Problem, Ex 1
Law of Sines - Application/Word Problem, Ex 1. In this video, we do a word/application problem that involves using the law of sines.
Lecture 115

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Law of Sines - Application / Word Problem, Ex 2
Law of Sines - Application/Word Problem, Ex 2. Just another word/application problem that involves using the Law of SInes.
Lecture 116

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Law of Sines - Application/Word Problem, Ex 3
Law of Sines - Application/Word Problem, Ex 3. Just another word/application problem that involves using the Law of SInes.
Lecture 117

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Heron's Formula, Example 1
Heron's Formula, Example 1. Here I use Heron's Formula to find the area of a triangle.
Lecture 118

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Heron's Formula, Ex 2
Heron's Formula, Example 2. Here I use Heron's Formula to help find the height of a triangle.
Lecture 119

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Heron's Formula, Example 3
Heron's Formula, Example 3. In this video, we use both the law of sines and also Heron's Formula to find the area of a triangle.
IX. Law of Cosines
Lecture 120

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Law of Cosines, Example 1
The Law of Cosines, Example 1. In this video, I give the formula for the Law of Cosines and use it to find the missing side length of a triangle.
Lecture 121

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Law of Cosines, Example 2
The Law of Cosines, Example 2. In this video, I give the formula for the Law of Cosines and use it to find the missing side length of a triangle.
Lecture 122

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Law of Cosines, Example 3
The Law of Cosines, Example 3. In this video, I give the formula for the Law of Cosines and use it to find the value of a missing angle.
Lecture 123

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Law of Cosines, Example 4
The Law of Cosines, Example 4. Here we use the law of cosines to help deduce an angle between the flightpath of two planes!
Lecture 124

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Law of Cosines, Example 5
Law of Cosines, Example 5. Just another example of finding the missing length of a triangle using the Law of Cosines.
Lecture 125

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Law of Cosines, Example 6
Law of Cosines, Example 6. In this video, we find how far a person is from a house by knowing that person's distance to someone else and the angle formed between them and the house.
Lecture 126

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Law of Cosines, Word Problem #1
Law of Cosines, Word Problem #1. Just a little word problem involving a parallelogram and some angles and side lengths.
X. Vectors
Lecture 127

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An Introduction to Vectors, Part 1
An introduction to vectors: magnitude, direction, length, component form are all discussed.
Lecture 128

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When Are Two Vectors Considered to Be the Same?
When are two vectors considered to be the same?
Lecture 129

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Magnitude and Direction of a Vector, Example 1
Magnitude and Direction of a Vector, Example 1. Here we find the magnitude (length) of some vectors and find the angle associated with them.
Lecture 130

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Magnitude and Direction of a Vector, Example 2
Magnitude and Direction of a Vector, Example 2. Here we find the magnitude (length) of some vectors and find the angle associated with them.
Lecture 131

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Magnitude and Direction of a Vector, Example 3
Magnitude and Direction of a Vector, Example 3. Here we find the magnitude (length) of one last vector and find the angle associated with them.
Lecture 132

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Vector Addition and Scalar Multiplication, Example 1
Vector Addition and Scalar Multiplication, Example 1. In this video, we look at vector addition and scalar multiplication algebraically using the component form of the vector. I do not graph the vectors in this video (but do in others).
Lecture 133

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Vector Addition and Scalar Multiplication, Example 2
Vector Addition and Scalar Multiplication, Example 2. In this video I add two vectors in component form and also sketch the vectors to illustrate how to add vectors graphically (very useful stuff!).
Lecture 134

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Finding the Components of a Vector, Ex 1
Finding the Components of a Vector, Ex 1. In this video, we are given the magnitude and direction angle for the vector and want to express the vector in component form.
Lecture 135

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Finding the Components of a Vector, Ex 2
Finding the Components of a Vector, Ex 2. In this video, we are given the magnitude and direction angle for the vector and want to express the vector in component form.
Lecture 136

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Finding a Unit Vector, Ex 1
Finding a Unit Vector, Ex 1. In this video I discuss the idea of a unit vector and show how to find it (divide the vector by its magnitude!).
Lecture 137

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Finding a Unit Vector, Ex 2
Finding a Unit Vector, Ex 2. In this video we find a unit vector associated with a given vector.
Lecture 138

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Word Problems Involving Velocity or Other Forces (Vectors), Ex 1
Word Problems Involving Velocity or Other Forces (Vectors), Ex 1. In this problem we do a word problem involving the bearing (direction) of a boat.
Lecture 139

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Word Problems Involving Velocity or Other Forces (Vectors), Ex 2
Word Problems Involving Velocity or Other Forces (Vectors), Ex 2. In this problem we are given the bearing and velocity of a plane and the bearing and velocity of the wind; we want to find out the actual velocity of the plane after taking the wind into consideration. (a nice little problem!)
Lecture 140

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Word Problems Involving Velocity or Other Forces (Vectors), Ex 3.
Word Problems Involving Velocity or Other Forces (Vectors), Ex 3. Here we know the force required to keep a box from sliding down a ramp; we want to know the angle of inclination of the ramp.
XI. Complex Numbers & Trigonometry
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Complex Numbers: Graphing and Finding the Modulus, Ex 1
Complex Numbers: Graphing and Finding the Modulus, Ex 1. In this video, I show how to graph a complex number and how to find the modulus of a complex number.
Lecture 142

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Complex Numbers: Graphing and Finding the Modulus, Ex 2
Complex Numbers: Graphing and Finding the Modulus, Ex 2. In this video, I show how to graph another complex number and how to find its modulus.
Lecture 143

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Expressing a Complex Number in Trigonometric or Polar Form, Ex 1
Expressing a Complex Number in Trigonometric or Polar Form, Ex 1. In this video, I show how to write a complex number in polar form. Example 1.
Lecture 144

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Expressing a Complex Number in Trigonometric or Polar Form, Ex 2
Expressing a Complex Number in Trigonometric or Polar Form, Ex 2. Just another example of writing a complex number in polar form.
Lecture 145

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Expressing a Complex Number in Trigonometric or Polar Form, Ex 3
Expressing a Complex Number in Trigonometric or Polar Form, Ex 3. One more example of writing a complex number in polar form.
Lecture 146

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Complex Numbers: Convert From Polar to Complex Form, Ex 1
Complex Numbers: Convert From Polar to Complex Form, Ex 1. In this video, we take a number in polar form and write it in complex form.
Lecture 147

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Complex Numbers: Multiplying and Dividing in Polar Form, Ex 1
Complex Numbers: Multiplying and Dividing in Polar Form, Ex 1. In this video, I give the formula for multiplication and division of two complex numbers that are in polar form.
Lecture 148

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Complex Numbers: Multiplying and Dividing in Polar Form, Ex 2
Complex Numbers: Multiplying and Dividing in Polar Form, Ex 2. In this video, I give the formula for multiplication and division of two complex numbers that are in polar form.
Lecture 149

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DeMoivre's Theorem: Raising a Complex Number to a Power, Ex 1
DeMoivre's Theorem: Raising a Complex Number to a Power, Ex 1. In this video I give DeMoivre's theorem and use it to raise a complex number to a power. Note that our number must be in polar form!
Lecture 150

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DeMoivre's Theorem: Raising a Complex Number to a Power, Ex 2
DeMoivre's Theorem: Raising a Complex Number to a Power, Ex 2. In this video, we want to multiply powers of two complex numbers. I use Demoivre's Theorem to help simplify.. Note that our number must be in polar form!
Lecture 151

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DeMoivre's Theorem: Raising a Complex Number to a Power, Ex 3
DeMoivre's Theorem: Raising a Complex Number to a Power, Ex 3. In this video, we want to raise a complex number to a power. I use Demoivre's Theorem to help simplify.. Note that our number must be in polar form!
Lecture 152

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Roots of Complex Numbers, Ex 1
Finding roots of complex numbers. Here I give the formula to find the n-th root of a complex number and use it to find the square roots of a number.
Lecture 153

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Roots of Complex Numbers, Ex 2
Finding roots of complex numbers, Ex 2. Here I give the formula to find the n-th root of a complex number and use it to find the square roots of a number. Note that the number must first be in polar form.
Lecture 154

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Roots of Complex Numbers, Ex 3
Finding roots of complex numbers, Ex 3. In this video, I find all of the cube roots of 64 (of course, 4 is one of the roots.... what are the others??!).
Lecture 155

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More Roots of Complex Numbers, Ex 1
More Roots of Complex Numbers, Ex 1. Here I find the square roots of a complex number.
Lecture 156

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More Roots of Complex Numbers, Ex 2
More Roots of Complex Numbers, Ex 2. Here I find the square roots of a complex number.
Lecture 157

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Roots of Unity, Example 1
Roots of Unity, Example 1. Here is give a little discussion about finding roots of unity and the unit circle.
Lecture 158

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Roots of Unity, Ex 2
Roots of Unity, Brief Question about finding the quadrant in which the roots belong.
XII. Polar Coordinates
Lecture 159

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Intro to Polar Coordinates, Ex 1
Intro to Polar Coordinates. Just a few quick questions related to the basics of polar coordinates.
Lecture 160

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Converting Between Polar and Rectangular (Cartesian) Coordinates, Ex 3
Converting Between Polar and Rectangular (Cartesian) Coordinates, Ex 3. In this video, I show how to convert from polar to cartesian form (I think these are easier than going from cartesian to polar form!).
Lecture 161

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Converting Between Polar and Rectangular Equations, Ex 1
Converting Between Polar and Rectangular Equations, Ex 1. In this video, I take one polar equation and write it in rectangular (cartesian) form.
Lecture 162

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Converting Between Polar and Rectangular Equations, Ex 2
Converting Between Polar and Rectangular Equations, Ex 2. In this video, I take some polar equations and write them in rectangular (cartesian) form.
Lecture 163

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Converting Between Polar and Rectangular Equations, Ex 3
Converting Between Polar and Rectangular Equations, Ex 3. In this video, we look at going taking our equations that are in rectangular form and put them in polar form.
Lecture 164

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Graphing Simple Polar Equations, Ex 1
Graphing Simple Polar Equations, Ex 1. Graphing polar curves can be tricky, but here I look at graphing some of the basic ones first!
Lecture 165

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Graphing Simple Polar Equations, Ex 2
Graphing Simple Polar Equations, Ex 2, In this video, I show the common trick of writing our polar equation in cartesian form so that we can (hopefully) recognize it as a common graph. In this case, our polar equation simply turns out to be a circle.
Lecture 166

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Graphing Special Polar Equations, Ex 1
Graphing Special Polar Equations, Ex 1. Just another example of taking a polar equation and putting it in cartesian form so that we can graph it more easily.
Lecture 167

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Graphing Special Polar Equations; How Many Petals Will a Graph Have?
Graphing Special Polar Equations, Ex 2. Many polar graphs have 'petals'. How many petals will a graph have? This problem addresses that question!
Lecture 168

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