# Pre-Calculus 6-9: Trigonometry Review

## Video Lectures

Displaying all 152 video lectures.
I. The Unit Circle
Lecture 1

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What Is The Unit Circle?
In this video I will introduce and explain the unit circle and the relationship of the sides and angles.
Lecture 2

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The Unit Circle and The Angle (Part 1 of 2)
In this video I will explain the unit circle and the relationship of the angles and the lengths of the arc.
Lecture 3

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The Unit Circle and The Angle (Part 2 of 2)
In this video I will explain the unit circle and the value of the (x,y) on the circle.
Lecture 4

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The Unit Circle and The Angle (30 and 60 Degrees)
In this video I will find the (x,y) value of the unit circle at 30 and 60 degrees.
Lecture 5

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The Unit Circle and The Signs of x and y
In this video I will find the signs of (x,y) in the 4 quadrants of the unit circle.
II. Trigonometric Functions
Lecture 6

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The Trigonometry Function: Sine Explained
In this video I will explain the trigonometry function: What is the sine of an angle?
Lecture 7

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The Trigonometry Function: Cosine Explained
In this video I will explain the trigonometry function: What is the cosine of an angle?
Lecture 8

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The Trigonometry Function: Tanget Explained
In this video I will explain the trigonometry function: What is the tangent of an angle?
Lecture 9

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The Trigonometry Function: Cotanget Explained
In this video I will explain the trigonometry function: What is the cotangent of an angle?
Lecture 10

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The Trigonometry Function: Secant Explained
In this video I will explain the trigonometry function: What is the secant of an angle?
Lecture 11

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The Trigonometry Function: Cosecant Explained
In this video I will explain the trigonometry function: What is the cosecant of an angle?
III. Trigonometric Angles
Lecture 12

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What Are Negative Angles?
In this video I will explain what are negative angles and how to convert them to a positive angle within the unit circle.
Lecture 13

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How to Convert Angles Greater Than 360?
In this video I will explain what are angles greater than 360 degrees and how to convert them to a positive angle within the unit circle.
Lecture 14

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What Are Odd and Even Functions?
In this video I will define and explains even and odd properties of trigonometry functions.
Lecture 15

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Fundamental Trig Idenities
In this video I will derive the basic fundamental trig identities.
Lecture 16

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Using the Unit Circle to Evaluate Trig Functions
In this video I will evaluate the trigonometric functions (sines and cosines) using the unit circle.
Lecture 17

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Using the Unit Circle to Evaluate Trig Functions
In this video I will evaluate the trigonometric functions (csc, sec, tan, and cot) using the unit circle.
Lecture 18

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Using the Unit Circle to Evaluate Trig Functions
In this video I will evaluate the trigonometric functions (sin, cos, tan, csc) using the unit circle.
IV. Reduction Formulas
Lecture 19

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Reduction Formula (1 of 4) Add/Subtract 2pi
In this video I will explain the reduction formula (add/subtract 2pi).
Lecture 20

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Reduction Formula (2 of 4) Add/Subtract pi
In this video I will explain the reduction formula (add/subtract pi).
Lecture 21

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Reduction Formula (3 of 4) Add pi/2
In this video I will explain the reduction formula (add pi/2).
Lecture 22

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Reduction Formula (4 of 4) Subtract pi/2
In this video I will explain the reduction formula (subtract pi/2).
V. Graphing Trigonometric Functions
Lecture 23

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Graphing y=sin(theta) (1 of 2)
In this video I will graph the trig function y=sin(theta) using a table of values.
Lecture 24

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Graphing y=sin(theta) (2 of 2) And the Unit Circle
In this video I will show how the unit circle relates to the graph of y=sin(theta).
Lecture 25

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Graphing y=cos(theta)
In this video I will graph the trig function y=cos(theta) using a table of values.
Lecture 26

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Graphing y=tan(theta)
In this video I will graph the trig function y=tan(theta) using a table of values.
Lecture 27

Play Video
Period of the Sine and Cosine Graphs
In this video I will review the periodicity of the sine and cosine functions.
Lecture 28

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The General Equation for Sine and Cosine
In this video I will take a closer look at the general form of the sine and cosine functions.
Lecture 29

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The General Equation for Sine and Cosine: Amplitude
In this video I will explain the amplitude of the general form of the sine and cosine functions.
Lecture 30

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The General Equation for Sine and Cosine: Period
In this video I will explain the period of the general form of the sine and cosine functions.
Lecture 31

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The General Equation for Sine and Cosine: Left/Right Shift
In this video I will explain the left/right shift of the general form of the sine and cosine functions.
Lecture 32

Play Video
The General Equation for Sine and Cosine: Up/Down Shift
THIS IS RE-UPLOAD OF A PREVIOUS VIDEO:
WHICH CONTAINED AN ERROR.

In this video I will explain the up/down shift of the general form of the sine and cosine functions.
Lecture 33

Play Video
Graphing Sum of Trigonometry Functions (1 of 2)
In this video I will graph the sum of the trig functions y=sinx and y=cosx.
Lecture 34

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Graphing Sum of Trigonometry Functions (2 of 2)
In this video I will graph the sum of the trig functions y1=cos2x and y2=2sinx.
Lecture 35

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Graphing the Negative of a Trig Function
In this video I will graph the negative of a trig function (y1=cosx, y2=-cosx, y1+y2=?).
Lecture 36

Play Video
Graphing the Product of a Trig Function (No Calculators!)
THIS IS RE-UPLOAD OF A PREVIOUS (36 of 54) VIDEO LOCATED AT:
WHICH CONTAINED AN ERROR.

In this video I will graph the product of the trig function y=xsinx (no calculators!).
Lecture 37

Play Video
Graphing the Product of a Trig Function (No Calculators!)
In this video I will graph the product of the trig function y=(x^2)cos10x (no calculators!).
Lecture 38

Play Video
Graphing the Product of a Trig Function (No Calculators!)
In this video I will graph the product of the trig function y=[e^(-x)]sin5x (no calculators!).
Lecture 39

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Graph the Function y=-(1/2)sinx
In this video I will graph the trig function y=-(1/2)sinx using the general form equation.
Lecture 40

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Graph the Function y=2+2cosx
In this video I will graph the trig function y=2+2cosx using the general form equation.
Lecture 41

Play Video
Find the Amplitude, Period, and Graph y=-3sin3x
In this video I will find A=?, P=? and sketch y=-3sin3x.
Lecture 42

Play Video
Find the Amplitude, Period, and Graph y=4cos[(1/2)x]
In this video I will find A=?, P=? and sketch y=4cos[(1/2)x].
Lecture 43

Play Video
Find the Amplitude, Period, and Graph y=cos[x-(pi/2)]
In this video I will find A=?, P=?, phase angle=? and sketch y=cos[x-(pi/2)].
Lecture 44

Play Video
Find the Amplitude, Period, and Graph y=3sin[(2x/3)-(pi/6)]
In this video I will find A=?, P=?, phase angle=? and sketch y=3sin[(2x/3)-(pi/6)].
Lecture 45

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Find the Amplitude, Period, and Graph y=2cos[3x+(pi/4)]-1
In this video I will find A=?, P=?, phase angle=? and sketch y=2cos[3x+(pi/4)]-1.
Lecture 46

Play Video
Find the Amplitude, Period, Phase Angle, and Write Equation
In this video I will find A=?, P=?, phase angle=?, C=? and write the equation given the graph.
Lecture 47

Play Video
Find the Amplitude, Period, Phase Angle, and Write Equation
In this video I will find A=?, P=?, phase angle=?, C=? and write the equation given the graph.
Lecture 48

Play Video
Find the Amplitude, Period, Phase Angle, and Write Equation
In this video I will find A=?, P=?, phase angle=?, C=? and write the equation given the graph.
Lecture 49

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Graph y=tan4x
In this video I will graph y=tan4x.
Lecture 50

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Graph y=csc2x
In this video I will graph y=csc2x.
VI. Inverse Trigonometric Functions
Lecture 51

Play Video
Inverse Sine Function
In this video I will graph the inverse sine function y=sin^-1(x).
Lecture 52

Play Video
Inverse Cosine Function
In this video I will graph the inverse cosine function y=cos^-1(x).
Lecture 53

Play Video
Inverse Tangent Function
In this video I will graph the inverse tangent function y=tan^-1(x).
Lecture 54

Play Video
Inverse Trigonometric Function: Don't Get Confused!
In this video I will caution and explain the confusing terms of inverse sine function, arcsine, inverse of a function,...
VII. The Right Triangle
Lecture 55

Play Video
In this video I will explain the right triangle and the relationship between degrees and radians.
Lecture 56

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Length of Arc (Circumference)
In this video I will explain the relationship between the arc length and angle of a circle.
Lecture 57

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Area of Sector (Circle)
In this video I will develop the general equation of an area of a sector (circle) and triangle.
Lecture 58

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Basics of Trigonometry
In this video I will explain the right triangle basics of sine, cosine, tangent,...
Lecture 59

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Basics of Trigonometry: Example
In this video I will explain by examples the practical uses of sines, cosines, tangents, cotangents, secants, and cosecants.
Lecture 60

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Basics of Trigonometry: Exercise 1
In this video I will find the legs of the right triangle given the hypotenuse and angle.
Lecture 61

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Basics of Trigonometry: Exercise 2
In this video I will find the legs of the right triangle given the hypotenuse and angle.
Lecture 62

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Basics of Trigonometry: Exercise 3
In this video I will find the adjacent side and angle given the hypotenuse and opposite side.
Lecture 63

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Basics of Trigonometry: Exercise 4
In this video I will find the opposite side and hypotenuse given the angle and adjacent side.
Lecture 64

Play Video
Inverse Trig Functions: Find Angle
In this video I will explain how to find the angle of a right triangle using the inverse trig functions.
Lecture 65

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Inverse Trig Functions: Ex. 1
In this video I will find the angle of a right triangle given the adjacent side and hypotenuse.
Lecture 66

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Inverse Trig Functions: Ex. 2
In this video I will find the angle of a right triangle given the adjacent and opposites sides.
Lecture 67

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Inverse Trig Functions: Summary
In this video I will summarize the uses of the inverse trig functions.
Lecture 68

Play Video
In this video I will find the sides (adjacent and opposite) of a right triangle given the angle and hypotenuse.
Lecture 69

Play Video
In this video I will find the hypotenuse and adjacent side given the angle and opposite side.
Lecture 70

Play Video
In this video I will find the angle and adjacent side given the hypotenuse and adjacent side.
Lecture 71

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Challenge Problem #1
In this video (challenge problem #1) I will find the portion of length of the opposite side.
Lecture 72

Play Video
Challenge Problem #2
In this video (challenge problem #2) I will find the hypotenuse of one of two triangles.
Lecture 73

Play Video
Challenge Problem #3
In this video (challenge problem #3) I will find the hypotenuse of one of two triangles.
Lecture 74

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Challenge Problem #4
In this video (challenge problem #4) I will find the leg of one of two triangles.
Lecture 75

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Height of Flag = ?
In this video I will find the height of a flag given the shadow and angle of the flag.
Lecture 76

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Distance to Near-By Star = ?
In this video I will use trigonometry to find the distance of a star.
Lecture 77

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Height of Building = ?
In this video I will find the height of a building observed from a window across from the building.
Lecture 78

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Distance Between Venus & Sun = ?
In this video I will use basic trig and the right triangle to find the distance between Venus and the Sun.
Lecture 79

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Circumference of the Planet = ?
In this video I will find the circumference of a distant planet with an orbiting Earth satellite.
Lecture 80

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Angle of Geosynchronous Satellite = ?
In this video I will find the angle of observation by a geosynchronous satellite.
VIII. The Law of Sines
Lecture 81

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Definition of The Law of Sines
In this video I will introduce, explain, and show how to apply The Law of Sines.
Lecture 82

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The Law of Sines Proved
In this video I will prove The Law of Sines.
Lecture 83

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Example of SSA (Side-Side-Angle)
In this video I will use The Law of Sines to solve for 2 angles and 1 side given SSA (side-side-angle).
Lecture 84

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Example of AAS (Angle-Angle-Side)
In this video I will use The Law of Sines to solve for 1 angle and 2 sides given AAS (angle-angle-side).
Lecture 85

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Caution: NO Solution cases with Law of Sines
In this video I will caution sometimes there are no solutions when using The Law of Sines.
Lecture 86

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Multiple Solutions with Law of Sines
In this video I will show sometimes there are multiple solutions when using The Law of Sines.
Lecture 87

Play Video
Finding the Height of the Satellite
In this video I will find the height of an Earth orbiting satellite.
Lecture 88

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Finding the Height of the Mountain
In this video I will show how to find the height a mountain while driving toward it.
IX. The Law of Cosines
Lecture 89

Play Video
What is the Law of Cosines?
In this video I will define The Law of Cosines.
Lecture 90

Play Video
Finding 3 Angles Given 3 Sides
In this video I will uses The Law of Cosines to find the 3 angles given the 3 sides, side-side-side (SSS) .
Lecture 91

Play Video
The Law of Cosines Proved
In this video I will prove The Law of Cosines.
Lecture 92

Play Video
Find Distance and Bearing of Airplane
In this video I will find the distance traveled and bearing of an airplane flying in wind.
Lecture 93

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Find Distance Between Ships
In this video I will find the distance between 2 ships traveling in different directions.
Lecture 94

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Heron's Formula: Intro
In this video I will introduce Heron's Formula and its applications.
Lecture 95

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Heron's Formula Proved
In this video I will prove Heron's Formula.
X. Trigonometric Identities
Lecture 96

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What are the basic trigonometric identities?
In this video I will introduce the first 3 basic trigonometric identities.
Lecture 97

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Cofunction Trigonometric Identities
In this video I will introduce and explain trigonometric cofunction identities.
Lecture 98

Play Video
Simplify the Trig Expression: 1
In this video I will simplify the expression (secx-cosx)/tanx=?
Lecture 99

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Simplify the Trig Expression: 2
In this video I will simplify the expression [(1+sinx)/cosx]+[cosx/(1+sinx)]=?
Lecture 100

Play Video
Verify the Identity: 1
In this video I will verify the identity (1-sinx)/(1+sinx)=(secx-tanx)^2.
Lecture 101

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Verify the Identity: 2
In this video I will verify the identity (1+tanx)/(1-tanx)=(cosx+sinx)/(cosx-sinx).
Lecture 102

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Verify the Identity: 3
In this video I will verify the identity (tanx-cotx)/(tan^2x-cot^2x)=sinxcosx.
Lecture 103

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Verify the Identity: 4
In this video I will verify the identity secx/(secx-tanx)=secx(secx+tanx).
Lecture 104

Play Video
In this video I will introduce trigonometric addition and subtraction formulas.
Lecture 105

Play Video
In this video I will prove the trigonometric addition formula for cosine: cos(A+B)=cosAcosB-sinAsinB.
Lecture 106

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Proof of Subtraction Formula (Cosine)
In this video I will prove the trigonometric subtraction formula for cosine: cos(A-B)=cosAcosB+sinAsinB.
Lecture 107

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Proving the Cofunction Idenity
In this video I will prove the trigonometric cofunction cos[(pi/2)-x]=sinx.
Lecture 108

Play Video
In this video I will prove the trigonometric addition formula for sine: sin(A+B)=sinAcosB+cosAsinB.
Lecture 109

Play Video
Proof of Subtraction Formula (Sine)
In this video I will prove the trigonometric subtraction formula for sine: sin(A-B)=sinAcosB-cosAsinB.
Lecture 110

Play Video
Proof of the Addition Formula (Tangent)
In this video I will prove the trigonometric addition formula for tangent: tan(A+B)=(tanA+tanB)/(1-tanAtanB).
Lecture 111

Play Video
Proof of the Subtraction Formula (Tangent)
In this video I will prove the trigonometric ubtraction formula for tangent: tan(A1B)=(tanA+tanB)/(1+tanAtanB).
Lecture 112

Play Video
Find sin75,...tan135 (Without a Calculator)
In this video I will solve sin75=? sin15=? cos105=? tan135=? without a calculator.
Lecture 113

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Proof Using Addition & Subtraction Formulas
In this video I will prove the trigonometric cofunction tan[(pi/2)-B]=cotB.
Lecture 114

Play Video
Proof Using Addition & Subtraction Formulas
In this video I will prove the trigonometric identity sin(A+B)-sin(A-B)=2cosAsinB.
Lecture 115

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Proof Using Addition & Subtraction Formulas
In this video I will prove the trigonometric identity tanA-tanB=sin(A-B)/(cosAcosB).
Lecture 116

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Proof Using Addition & Subtraction Formulas
In this video I will prove the trigonometric identity [sin(A+B)-sin(A-B)]/[cos(A+B)+cos(A-B)]=tanB.
Lecture 117

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Double Angle Formula: Introduction
In this video I will introduce the double angle formulas sin2A, cos2A, tan2A.
Lecture 118

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Double Angle Formula Proved: Sine
In this video I will prove the double angle formula sin2A=2sinAcosA.
Lecture 119

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Double Angle Formula Proved: Cosine
In this video I will prove the double angle formula cos2A=cos^2(A)-sin^2(A).
Lecture 120

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Double Angle Formula Proved: Tangent
In this video I will prove the double angle formula tan2A=2tanA/(1-tan^2(A).
Lecture 121

Play Video
Simplifying Triple Angles to a Single Angle
In this video I will solve the triple angle formula cos3x=? to a single angle.
Lecture 122

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Formula for Lowering Power cos^2(x)=?
In this video I will show how to lower the power or the trigonometric function cos^2(x)=?
Lecture 123

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Formula for Lowering Power sin^2(x)=?
In this video I will show how to lower the power or the trigonometric function sin^2(x)=?
Lecture 124

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Formula for Lowering Power tan^2(x)=?
In this video I will show how to lower the power or the trigonometric function tan^2(x)=?
Lecture 125

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Proof sin^2(x)=(1-cos2x)/2
In this video I will prove sin^2(x)=(1-cos2x)/2.
Lecture 126

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Proof cos^2(x)=(1+cos2x)/2
In this video I will prove cos^2(x)=(1+cos2x)/2.
Lecture 127

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Proof Half Angle Formula: sin(x/2)
In this video I will introduce the half-angle formula sin(x/2)=?
Lecture 128

Play Video
Proof Half Angle Formula: cos(x/2)
In this video I will introduce the half-angle formula cos(x/2)=?
Lecture 129

Play Video
Proof Half Angle Formula: tan(x/2)
In this video I will introduce the half-angle formula tan(x/2)=?
Lecture 130

Play Video
Product to Sum Formula 1
In this video I will prove sinAcosB=(1/2)[sin(A+B)+sin(A-B)] and cosAsinB=1/2)[sin(A+B)-sin(A-B)].
Lecture 131

Play Video
Product to Sum Formula 2
In this video I will prove cosAcosB=(1/2)[cos(A+B)+cos(A-B)] and sinAsinB=1/2)[cos(A+B)-cos(A-B)].
Lecture 132

Play Video
Sum to Product Formula 1
In this video I will prove sinx+siny=2sin[(x+y)/2]cos[(x-y)/2] and sinx-siny=2cos[(x+y)/2]sin[(x-y)/2].
Lecture 133

Play Video
Sum to Product Formula 2
In this video I will prove cosx+cosy=2cos[(x+y)/2]cos[(x-y)/2] and cosx-cosy=-2sin[(x+y)/2]sin[(x-y)/2].
Lecture 134

Play Video
Write sin(2x)cos3x as a Sum
In this video I will show how to convert sin(2x)cos3x=? (as a sum).
Lecture 135

Play Video
Write cos4x-cos6x as a Product
In this video I will show how to convert cos(4x)-cos(6x)=? (as a product).
Lecture 136

Play Video
Prove cos^4(x)-sin^4(x)=cos2x
In this video I will prove cos^4(x)-sin^4(x)=cos2x.
Lecture 137

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Prove [sinx+sin(5x)]/[cosx+cos(5x)]=tan3x
In this video I will prove [sinx+sin(5x)]/[cosx+cos(5x)]=tan3x.
Lecture 138

Play Video
Prove (sinA+sinB)/(cosA+cosB)=tan[(A+B)/2]
In this video I will prove (sinA+sinB)/(cosA+cosB)=tan[(A+B)/2].
Lecture 139

Play Video
Prove sin(4x)/sinx=4cosxcos(2x)
In this video I will prove sin(4x)/sinx=4cosxcos(2x).
Lecture 140

Play Video
Solve cos(theta)+1=0, theta=?
In this video I will solve cos(theta)+1=0, theta=?
Lecture 141

Play Video
Solve 3sin(theta)-1=0, theta=?
In this video I will solve 3sin(theta)-1=0, theta=?
Lecture 142

Play Video
Solve tan^2(theta)-4=0, theta=?
In this video I will solve tan^2(theta)-4=0, theta=?
Lecture 143

Play Video
Solve 2sin^2(theta)-sin(theta)-1=0, theta=?
In this video I will solve 2sin^2(theta)-sin(theta)-1=0, theta=?
Lecture 144

Play Video
Solve 2cos^2(theta)-7cos(theta)+3=0, theta=?
In this video I will solve 2cos^2(theta)-7cos(theta)+3=0, theta=?
Lecture 145

Play Video
Solve cos(x)sin(x)-2cos(x)=0, x=?
This video is an error-free video of "Trig Identities (50 of 57)". The video with the error is located at:

In this video I will solve cos(theta)sin(theta)-2cos(theta)=0, theta=?
Lecture 146

Play Video
Solve 3tan(x)sin(x)-2tan(x)=0, x=?
In this video I will solve 3tan(theta)sin(theta)-2tan(theta)=0, theta=?
Lecture 147

Play Video
Solve 3tan^3(theta)=tan(theta), theta=?
In this video I will solve 3tan^3(theta)=tan(theta), theta=?
Lecture 148

Play Video
Solve sin(2theta)+cos(theta)=0, theta=?
In this video I will solve sin(2theta)+cos(theta)=0, theta=?
Lecture 149

Play Video
Solve sin(theta)+sin(3theta)=0, theta=?
In this video I will solve sin(theta)+sin(3theta)=0, theta=?
Lecture 150

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Solve 2cos(3theta)=1, theta=?
In this video I will solve 2cos(3theta)=1, theta=?
Lecture 151

Play Video
Solve sin(2theta)=3cos(2theta), theta=?
In this video I will solve sin(2theta)=3cos(2theta), theta=?
Lecture 152

Play Video
Solve 2sin(x)tan(x)-tan(x)=1-2sin(x), x=?
In this video I will solve 2sin(theta)tan(theta)-tan(theta)=1-2sin(theta), theta=?