Trigonometry & Complex Numbers
Video Lectures
Displaying all 168 video lectures.
I. Angles and Arc Length | |
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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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
Degrees and Radians Degrees and Radians - Converting from Degrees to Radians! Many examples! For more free math videos, visit http://PatrickJMT.com |
Lecture 23 Play Video |
A Way to remember the Entire Unit Circle for Trigonometry Where Do These Values Come From? https://www.youtube.com/watch?v=3GgO7Q_kg8Q Need a LIVE tutor to help answer a question? Check out the people at http://www.tutor.com/signup?AdDist=1&ExAdId=90fddaff-89aa-4a... for a FREE 30 minute session! 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. Thanks for watching and please subscribe! Visit PatrickJMT.com and ' like ' it! :) A way to remember the Entire Unit Circle for Trigonometry. This is the way that I remember the unit circle. |
Lecture 24 Play Video |
A Trick to Remember Values on The Unit Circle Need a LIVE tutor to help answer a question? Check out the people at http://www.tutor.com/signup?AdDist=1&ExAdId=90fddaff-89aa-4a... for a FREE 30 minute session! 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. For more free math videos visit http://JustMathTutoring.com |
Lecture 25 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
Graphing Sine and Cosine with Phase (Horizontal) Shifts, Example 2 Need a LIVE tutor to help answer a question? Check out the people at http://www.tutor.com/signup?AdDist=1&ExAdId=90fddaff-89aa-4a... for a FREE 30 minute session! In this video, I graph a trigonometric function by graphing the original and then applying the phase shift. |
Lecture 42 Play Video |
Trigonometric Functions and Graphing: Amplitude, Period, Vertical and Horizontal Shifts, Ex 2 Need a LIVE tutor to help answer a question? Check out the people at http://www.tutor.com/signup?AdDist=1&ExAdId=90fddaff-89aa-4a... for a FREE 30 minute session! 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 Play Video |
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 Play Video |
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 Play Video |
Basic Questions Related to Tangent, Cotangent, Secant, Cosecant, Ex 4 Basic Questions Related to Tangent, Cotangent, Secant, Cosecant, Ex 4. |
Lecture 46 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
Simplifying Trigonometric Expressions Involving Fractions, Example 2 Simplifying Trigonometric Expressions Involving Fractions, Example 2 |
Lecture 56 Play Video |
Simplifying Products of Binomials Involving Trigonometric Functions, Ex 1 Simplifying Products of Binomials Involving Trigonometric Functions, Ex 1 |
Lecture 57 Play Video |
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 Play Video |
Examples with Trigonometric Functions: Even, Odd or Neither, Example 1 Examples with Trigonometric Functions: Even, Odd or Neither, Example 1 |
Lecture 61 Play Video |
Examples with Trigonometric Functions: Even, Odd or Neither, Example 2 Examples with Trigonometric Functions: Even, Odd or Neither, Example 2 |
Lecture 62 Play Video |
Examples with Trigonometric Functions: Even, Odd or Neither, Example 3 Examples with Trigonometric Functions: Even, Odd or Neither, Example 3 |
Lecture 63 Play Video |
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 Play Video |
Proving an Identity, Example 2 Proving an Identity, Example 2 |
Lecture 66 Play Video |
Proving an Identity - Other Examples, Example 1 Proving an Identity - Other Examples, Example 1 |
Lecture 67 Play Video |
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 Play Video |
Solving a Trigonometric Equation by Factoring, Example 2 Solving a Trigonometric Equation by Factoring, Example 2 |
Lecture 73 Play Video |
Solving a Trigonometric Equation by Factoring, Example 3 Solving a Trigonometric Equation by Factoring, Example 3 |
Lecture 74 Play Video |
Solving Trigonometric Equation, Harder Example - Example 1 Solving Trigonometric Equations with Coefficients in the Argument - Example 1 |
Lecture 75 Play Video |
Solving Trigonometric Equation, Harder Example - Example 2 Solving Trigonometric Equations with Coefficients in the Argument - Example 2 |
Lecture 76 Play Video |
Solving Trigonometric Equation , Harder Exampe - Example 3 Solving Trigonometric Equations with Coefficients in the Argument - Example 3 |
Lecture 77 Play Video |
Solving Trigonometric Equations Using the Quadratic Formula - Example 1 Solving Trigonometric Equations Using the Quadratic Formula - Example 1 |
Lecture 78 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
Cofunction Identities, Example 2 Cofunction Identities, Example 2. In this video I use a cofunction identity to simplify an expression. |
Lecture 101 Play Video |
Cofunction Identities, Example 3 Cofunction Identities, Example 3. In this video I use a cofunction identity to simplify an expression. |
Lecture 102 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
An Introduction to Vectors, Part 1 An introduction to vectors: magnitude, direction, length, component form are all discussed. |
Lecture 128 Play Video |
When Are Two Vectors Considered to Be the Same? When are two vectors considered to be the same? |
Lecture 129 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 | |
Lecture 141 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
Roots of Unity, Ex 2 Roots of Unity, Brief Question about finding the quadrant in which the roots belong. |
XII. Polar Coordinates | |
Lecture 159 Play Video |
Intro to Polar Coordinates, Ex 1 Intro to Polar Coordinates. Just a few quick questions related to the basics of polar coordinates. |
Lecture 160 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
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 Play Video |
Basic Info About a Limacon Graphing a Limacon - Just some info about how to find x and y intercepts for a limacon (I do not actually graph it, sorry!). |