Pre-Calculus 6-9: Trigonometry Review

Video Lectures

Displaying all 152 video lectures.
I. The Unit Circle
Lecture 1
What Is The Unit Circle?
Play Video		 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
The Unit Circle and The Angle (Part 1 of 2)
Play Video		 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
The Unit Circle and The Angle (Part 2 of 2)
Play Video		 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
The Unit Circle and The Angle (30 and 60 Degrees)
Play Video		 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
The Unit Circle and The Signs of x and y
Play Video		 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
The Trigonometry Function: Sine Explained
Play Video		 The Trigonometry Function: Sine Explained
In this video I will explain the trigonometry function: What is the sine of an angle?
Lecture 7
The Trigonometry Function: Cosine Explained
Play Video		 The Trigonometry Function: Cosine Explained
In this video I will explain the trigonometry function: What is the cosine of an angle?
Lecture 8
The Trigonometry Function: Tanget Explained
Play Video		 The Trigonometry Function: Tanget Explained
In this video I will explain the trigonometry function: What is the tangent of an angle?
Lecture 9
The Trigonometry Function: Cotanget Explained
Play Video		 The Trigonometry Function: Cotanget Explained
In this video I will explain the trigonometry function: What is the cotangent of an angle?
Lecture 10
The Trigonometry Function: Secant Explained
Play Video		 The Trigonometry Function: Secant Explained
In this video I will explain the trigonometry function: What is the secant of an angle?
Lecture 11
The Trigonometry Function: Cosecant Explained
Play Video		 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
What Are Negative Angles?
Play Video		 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
How to Convert Angles Greater Than 360?
Play Video		 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
What Are Odd and Even Functions?
Play Video		 What Are Odd and Even Functions?
In this video I will define and explains even and odd properties of trigonometry functions.
Lecture 15
Fundamental Trig Idenities
Play Video		 Fundamental Trig Idenities
In this video I will derive the basic fundamental trig identities.
Lecture 16
Using the Unit Circle to Evaluate Trig Functions
Play Video		 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
Using the Unit Circle to Evaluate Trig Functions
Play Video		 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
Using the Unit Circle to Evaluate Trig Functions
Play Video		 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
Reduction Formula (1 of 4) Add/Subtract 2pi
Play Video		 Reduction Formula (1 of 4) Add/Subtract 2pi
In this video I will explain the reduction formula (add/subtract 2pi).
Lecture 20
Reduction Formula (2 of 4) Add/Subtract pi
Play Video		 Reduction Formula (2 of 4) Add/Subtract pi
In this video I will explain the reduction formula (add/subtract pi).
Lecture 21
Reduction Formula (3 of 4) Add pi/2
Play Video		 Reduction Formula (3 of 4) Add pi/2
In this video I will explain the reduction formula (add pi/2).
Lecture 22
Reduction Formula (4 of 4) Subtract pi/2
Play Video		 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
Graphing y=sin(theta) (1 of 2)
Play Video		 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
Graphing y=sin(theta) (2 of 2) And the Unit Circle
Play Video		 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
Graphing y=cos(theta)
Play Video		 Graphing y=cos(theta)
In this video I will graph the trig function y=cos(theta) using a table of values.
Lecture 26
Graphing y=tan(theta)
Play Video		 Graphing y=tan(theta)
In this video I will graph the trig function y=tan(theta) using a table of values.
Lecture 27
Period of the Sine and Cosine Graphs
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
The General Equation for Sine and Cosine
Play Video		 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
The General Equation for Sine and Cosine: Amplitude
Play Video		 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
The General Equation for Sine and Cosine: Period
Play Video		 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
The General Equation for Sine and Cosine: Left/Right Shift
Play Video		 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
The General Equation for Sine and Cosine: Up/Down Shift
Play Video		 The General Equation for Sine and Cosine: Up/Down Shift
THIS IS RE-UPLOAD OF A PREVIOUS VIDEO:
https://www.youtube.com/watch?v=kGQ6SWJmpG4
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
Graphing Sum of Trigonometry Functions (1 of 2)
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
Graphing Sum of Trigonometry Functions (2 of 2)
Play Video		 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
Graphing the Negative of a Trig Function
Play Video		 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
Graphing the Product of a Trig Function (No Calculators!)
Play Video		 Graphing the Product of a Trig Function (No Calculators!)
THIS IS RE-UPLOAD OF A PREVIOUS (36 of 54) VIDEO LOCATED AT:
https://www.youtube.com/watch?v=ws22xUAGTAA
WHICH CONTAINED AN ERROR.



In this video I will graph the product of the trig function y=xsinx (no calculators!).
Lecture 37
Graphing the Product of a Trig Function (No Calculators!)
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
Graphing the Product of a Trig Function (No Calculators!)
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
Graph the Function y=-(1/2)sinx
Play Video		 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
Graph the Function y=2+2cosx
Play Video		 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
Find the Amplitude, Period, and Graph y=-3sin3x
Play Video		 Find the Amplitude, Period, and Graph y=-3sin3x
In this video I will find A=?, P=? and sketch y=-3sin3x.
Lecture 42
Find the Amplitude, Period, and Graph y=4cos[(1/2)x]
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
Find the Amplitude, Period, and Graph y=cos[x-(pi/2)]
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
Find the Amplitude, Period, and Graph y=3sin[(2x/3)-(pi/6)]
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
Find the Amplitude, Period, and Graph y=2cos[3x+(pi/4)]-1
Play Video		 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
Find the Amplitude, Period, Phase Angle, and Write Equation
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
Find the Amplitude, Period, Phase Angle, and Write Equation
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
Find the Amplitude, Period, Phase Angle, and Write Equation
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
Graph y=tan4x
Play Video		 Graph y=tan4x
In this video I will graph y=tan4x.
Lecture 50
Graph y=csc2x
Play Video		 Graph y=csc2x
In this video I will graph y=csc2x.
VI. Inverse Trigonometric Functions
Lecture 51
Inverse Sine Function
Play Video		 Inverse Sine Function
In this video I will graph the inverse sine function y=sin^-1(x).
Lecture 52
Inverse Cosine Function
Play Video		 Inverse Cosine Function
In this video I will graph the inverse cosine function y=cos^-1(x).
Lecture 53
Inverse Tangent Function
Play Video		 Inverse Tangent Function
In this video I will graph the inverse tangent function y=tan^-1(x).
Lecture 54
Inverse Trigonometric Function: Don't Get Confused!
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
Angle In Radians
Play Video		 Angle In Radians
In this video I will explain the right triangle and the relationship between degrees and radians.
Lecture 56
Length of Arc (Circumference)
Play Video		 Length of Arc (Circumference)
In this video I will explain the relationship between the arc length and angle of a circle.
Lecture 57
Area of Sector (Circle)
Play Video		 Area of Sector (Circle)
In this video I will develop the general equation of an area of a sector (circle) and triangle.
Lecture 58
Basics of Trigonometry
Play Video		 Basics of Trigonometry
In this video I will explain the right triangle basics of sine, cosine, tangent,...
Lecture 59
Basics of Trigonometry: Example
Play Video		 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
Basics of Trigonometry: Exercise 1
Play Video		 Basics of Trigonometry: Exercise 1
In this video I will find the legs of the right triangle given the hypotenuse and angle.
Lecture 61
Basics of Trigonometry: Exercise 2
Play Video		 Basics of Trigonometry: Exercise 2
In this video I will find the legs of the right triangle given the hypotenuse and angle.
Lecture 62
Basics of Trigonometry: Exercise 3
Play Video		 Basics of Trigonometry: Exercise 3
In this video I will find the adjacent side and angle given the hypotenuse and opposite side.
Lecture 63
Basics of Trigonometry: Exercise 4
Play Video		 Basics of Trigonometry: Exercise 4
In this video I will find the opposite side and hypotenuse given the angle and adjacent side.
Lecture 64
Inverse Trig Functions: Find Angle
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
Inverse Trig Functions: Ex. 1
Play Video		 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
Inverse Trig Functions: Ex. 2
Play Video		 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
Inverse Trig Functions: Summary
Play Video		 Inverse Trig Functions: Summary
In this video I will summarize the uses of the inverse trig functions.
Lecture 68
Find All Unknowns (Adj=? Opp=?)
Play Video		 Find All Unknowns (Adj=? Opp=?)
In this video I will find the sides (adjacent and opposite) of a right triangle given the angle and hypotenuse.
Lecture 69
Find All Unknowns (Adj=? Hyp=?)
Play Video		 Find All Unknowns (Adj=? Hyp=?)
In this video I will find the hypotenuse and adjacent side given the angle and opposite side.
Lecture 70
Find All Unknowns (Adj=? Angle=?)
Play Video		 Find All Unknowns (Adj=? Angle=?)
In this video I will find the angle and adjacent side given the hypotenuse and adjacent side.
Lecture 71
Challenge Problem #1
Play Video		 Challenge Problem #1
In this video (challenge problem #1) I will find the portion of length of the opposite side.
Lecture 72
Challenge Problem #2
Play Video		 Challenge Problem #2
In this video (challenge problem #2) I will find the hypotenuse of one of two triangles.
Lecture 73
Challenge Problem #3
Play Video		 Challenge Problem #3
In this video (challenge problem #3) I will find the hypotenuse of one of two triangles.
Lecture 74
Challenge Problem #4
Play Video		 Challenge Problem #4
In this video (challenge problem #4) I will find the leg of one of two triangles.
Lecture 75
Height of Flag = ?
Play Video		 Height of Flag = ?
In this video I will find the height of a flag given the shadow and angle of the flag.
Lecture 76
Distance to Near-By Star = ?
Play Video		 Distance to Near-By Star = ?
In this video I will use trigonometry to find the distance of a star.
Lecture 77
Height of Building = ?
Play Video		 Height of Building = ?
In this video I will find the height of a building observed from a window across from the building.
Lecture 78
Distance Between Venus & Sun = ?
Play Video		 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
Circumference of the Planet = ?
Play Video		 Circumference of the Planet = ?
In this video I will find the circumference of a distant planet with an orbiting Earth satellite.
Lecture 80
Angle of Geosynchronous Satellite = ?
Play Video		 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
Definition of The Law of Sines
Play Video		 Definition of The Law of Sines
In this video I will introduce, explain, and show how to apply The Law of Sines.
Lecture 82
The Law of Sines Proved
Play Video		 The Law of Sines Proved
In this video I will prove The Law of Sines.
Lecture 83
Example of SSA (Side-Side-Angle)
Play Video		 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
Example of AAS (Angle-Angle-Side)
Play Video		 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
Caution: NO Solution cases with Law of Sines
Play Video		 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
Multiple Solutions with Law of Sines
Play Video		 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
Finding the Height of the Satellite
Play Video		 Finding the Height of the Satellite
In this video I will find the height of an Earth orbiting satellite.
Lecture 88
Finding the Height of the Mountain
Play Video		 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
What is the Law of Cosines?
Play Video		 What is the Law of Cosines?
In this video I will define The Law of Cosines.
Lecture 90
Finding 3 Angles Given 3 Sides
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
The Law of Cosines Proved
Play Video		 The Law of Cosines Proved
In this video I will prove The Law of Cosines.
Lecture 92
Find Distance and Bearing of Airplane
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
Find Distance Between Ships
Play Video		 Find Distance Between Ships
In this video I will find the distance between 2 ships traveling in different directions.
Lecture 94
Heron's Formula: Intro
Play Video		 Heron's Formula: Intro
In this video I will introduce Heron's Formula and its applications.
Lecture 95
Heron's Formula Proved
Play Video		 Heron's Formula Proved
In this video I will prove Heron's Formula.
X. Trigonometric Identities
Lecture 96
What are the basic trigonometric identities?
Play Video		 What are the basic trigonometric identities?
In this video I will introduce the first 3 basic trigonometric identities.
Lecture 97
Cofunction Trigonometric Identities
Play Video		 Cofunction Trigonometric Identities
In this video I will introduce and explain trigonometric cofunction identities.
Lecture 98
Simplify the Trig Expression: 1
Play Video		 Simplify the Trig Expression: 1
In this video I will simplify the expression (secx-cosx)/tanx=?
Lecture 99
Simplify the Trig Expression: 2
Play Video		 Simplify the Trig Expression: 2
In this video I will simplify the expression [(1+sinx)/cosx]+[cosx/(1+sinx)]=?
Lecture 100
Verify the Identity: 1
Play Video		 Verify the Identity: 1
In this video I will verify the identity (1-sinx)/(1+sinx)=(secx-tanx)^2.
Lecture 101
Verify the Identity: 2
Play Video		 Verify the Identity: 2
In this video I will verify the identity (1+tanx)/(1-tanx)=(cosx+sinx)/(cosx-sinx).
Lecture 102
Verify the Identity: 3
Play Video		 Verify the Identity: 3
In this video I will verify the identity (tanx-cotx)/(tan^2x-cot^2x)=sinxcosx.
Lecture 103
Verify the Identity: 4
Play Video		 Verify the Identity: 4
In this video I will verify the identity secx/(secx-tanx)=secx(secx+tanx).
Lecture 104
Addition and Subtraction Formulas
Play Video		 Addition and Subtraction Formulas
In this video I will introduce trigonometric addition and subtraction formulas.
Lecture 105
Proof of Addition Formula (Cosine)
Play Video		 Proof of Addition Formula (Cosine)
In this video I will prove the trigonometric addition formula for cosine: cos(A+B)=cosAcosB-sinAsinB.
Lecture 106
Proof of Subtraction Formula (Cosine)
Play Video		 Proof of Subtraction Formula (Cosine)
In this video I will prove the trigonometric subtraction formula for cosine: cos(A-B)=cosAcosB+sinAsinB.
Lecture 107
Proving the Cofunction Idenity
Play Video		 Proving the Cofunction Idenity
In this video I will prove the trigonometric cofunction cos[(pi/2)-x]=sinx.
Lecture 108
Proof of Addition Formula (Sine)
Play Video		 Proof of Addition Formula (Sine)
In this video I will prove the trigonometric addition formula for sine: sin(A+B)=sinAcosB+cosAsinB.
Lecture 109
Proof of Subtraction Formula (Sine)
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
Proof of the Addition Formula (Tangent)
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
Proof of the Subtraction Formula (Tangent)
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
Find sin75,...tan135 (Without a Calculator)
Play Video		 Find sin75,...tan135 (Without a Calculator)
In this video I will solve sin75=? sin15=? cos105=? tan135=? without a calculator.
Lecture 113
Proof Using Addition & Subtraction Formulas
Play Video		 Proof Using Addition & Subtraction Formulas
In this video I will prove the trigonometric cofunction tan[(pi/2)-B]=cotB.
Lecture 114
Proof Using Addition & Subtraction Formulas
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
Proof Using Addition & Subtraction Formulas
Play Video		 Proof Using Addition & Subtraction Formulas
In this video I will prove the trigonometric identity tanA-tanB=sin(A-B)/(cosAcosB).
Lecture 116
Proof Using Addition & Subtraction Formulas
Play Video		 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
Double Angle Formula: Introduction
Play Video		 Double Angle Formula: Introduction
In this video I will introduce the double angle formulas sin2A, cos2A, tan2A.
Lecture 118
Double Angle Formula Proved: Sine
Play Video		 Double Angle Formula Proved: Sine
In this video I will prove the double angle formula sin2A=2sinAcosA.
Lecture 119
Double Angle Formula Proved: Cosine
Play Video		 Double Angle Formula Proved: Cosine
In this video I will prove the double angle formula cos2A=cos^2(A)-sin^2(A).
Lecture 120
Double Angle Formula Proved: Tangent
Play Video		 Double Angle Formula Proved: Tangent
In this video I will prove the double angle formula tan2A=2tanA/(1-tan^2(A).
Lecture 121
Simplifying Triple Angles to a Single Angle
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
Formula for Lowering Power cos^2(x)=?
Play Video		 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
Formula for Lowering Power sin^2(x)=?
Play Video		 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
Formula for Lowering Power tan^2(x)=?
Play Video		 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
Proof sin^2(x)=(1-cos2x)/2
Play Video		 Proof sin^2(x)=(1-cos2x)/2
In this video I will prove sin^2(x)=(1-cos2x)/2.
Lecture 126
Proof cos^2(x)=(1+cos2x)/2
Play Video		 Proof cos^2(x)=(1+cos2x)/2
In this video I will prove cos^2(x)=(1+cos2x)/2.
Lecture 127
Proof Half Angle Formula: sin(x/2)
Play Video		 Proof Half Angle Formula: sin(x/2)
In this video I will introduce the half-angle formula sin(x/2)=?
Lecture 128
Proof Half Angle Formula: cos(x/2)
Play Video		 Proof Half Angle Formula: cos(x/2)
In this video I will introduce the half-angle formula cos(x/2)=?
Lecture 129
Proof Half Angle Formula: tan(x/2)
Play Video		 Proof Half Angle Formula: tan(x/2)
In this video I will introduce the half-angle formula tan(x/2)=?
Lecture 130
Product to Sum Formula 1
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
Product to Sum Formula 2
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
Sum to Product Formula 1
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
Sum to Product Formula 2
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
Write sin(2x)cos3x as a Sum
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
Write cos4x-cos6x as a Product
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
Prove cos^4(x)-sin^4(x)=cos2x
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
Prove [sinx+sin(5x)]/[cosx+cos(5x)]=tan3x
Play Video		 Prove [sinx+sin(5x)]/[cosx+cos(5x)]=tan3x
In this video I will prove [sinx+sin(5x)]/[cosx+cos(5x)]=tan3x.
Lecture 138
Prove (sinA+sinB)/(cosA+cosB)=tan[(A+B)/2]
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
Prove sin(4x)/sinx=4cosxcos(2x)
Play Video		 Prove sin(4x)/sinx=4cosxcos(2x)
In this video I will prove sin(4x)/sinx=4cosxcos(2x).
Lecture 140
Solve cos(theta)+1=0, theta=?
Play Video		 Solve cos(theta)+1=0, theta=?
In this video I will solve cos(theta)+1=0, theta=?
Lecture 141
Solve 3sin(theta)-1=0, theta=?
Play Video		 Solve 3sin(theta)-1=0, theta=?
In this video I will solve 3sin(theta)-1=0, theta=?
Lecture 142
Solve tan^2(theta)-4=0, theta=?
Play Video		 Solve tan^2(theta)-4=0, theta=?
In this video I will solve tan^2(theta)-4=0, theta=?
Lecture 143
Solve 2sin^2(theta)-sin(theta)-1=0, theta=?
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
Solve 2cos^2(theta)-7cos(theta)+3=0, theta=?
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
Solve cos(x)sin(x)-2cos(x)=0, x=?
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:
https://www.youtube.com/watch?v=j60yiSvan8Y



In this video I will solve cos(theta)sin(theta)-2cos(theta)=0, theta=?
Lecture 146
Solve 3tan(x)sin(x)-2tan(x)=0, x=?
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
Solve 3tan^3(theta)=tan(theta), theta=?
Play Video		 Solve 3tan^3(theta)=tan(theta), theta=?
In this video I will solve 3tan^3(theta)=tan(theta), theta=?
Lecture 148
Solve sin(2theta)+cos(theta)=0, theta=?
Play Video		 Solve sin(2theta)+cos(theta)=0, theta=?
In this video I will solve sin(2theta)+cos(theta)=0, theta=?
Lecture 149
Solve sin(theta)+sin(3theta)=0, theta=?
Play Video		 Solve sin(theta)+sin(3theta)=0, theta=?
In this video I will solve sin(theta)+sin(3theta)=0, theta=?
Lecture 150
Solve 2cos(3theta)=1, theta=?
Play Video		 Solve 2cos(3theta)=1, theta=?
In this video I will solve 2cos(3theta)=1, theta=?
Lecture 151
Solve sin(2theta)=3cos(2theta), theta=?
Play Video		 Solve sin(2theta)=3cos(2theta), theta=?
In this video I will solve sin(2theta)=3cos(2theta), theta=?
Lecture 152
Solve 2sin(x)tan(x)-tan(x)=1-2sin(x), x=?
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=?