Pre-Calculus 6-9: Trigonometry Review
Video Lectures
Displaying all 152 video lectures.
I. The Unit Circle | |
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Lecture 1 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 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 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 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 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 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 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 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 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 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 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 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 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 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 Play Video |
Fundamental Trig Idenities In this video I will derive the basic fundamental trig identities. |
Lecture 16 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 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 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 Play Video |
Reduction Formula (1 of 4) Add/Subtract 2pi In this video I will explain the reduction formula (add/subtract 2pi). |
Lecture 20 Play Video |
Reduction Formula (2 of 4) Add/Subtract pi In this video I will explain the reduction formula (add/subtract pi). |
Lecture 21 Play Video |
Reduction Formula (3 of 4) Add pi/2 In this video I will explain the reduction formula (add pi/2). |
Lecture 22 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 Play Video |
Graph y=tan4x In this video I will graph y=tan4x. |
Lecture 50 Play Video |
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 |
Angle In Radians In this video I will explain the right triangle and the relationship between degrees and radians. |
Lecture 56 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 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 Play Video |
Basics of Trigonometry In this video I will explain the right triangle basics of sine, cosine, tangent,... |
Lecture 59 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 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 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 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 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 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 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 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 Play Video |
Inverse Trig Functions: Summary In this video I will summarize the uses of the inverse trig functions. |
Lecture 68 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 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 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 Play Video |
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 Play Video |
Challenge Problem #4 In this video (challenge problem #4) I will find the leg of one of two triangles. |
Lecture 75 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 Play Video |
Distance to Near-By Star = ? In this video I will use trigonometry to find the distance of a star. |
Lecture 77 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 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 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 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 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 Play Video |
The Law of Sines Proved In this video I will prove The Law of Sines. |
Lecture 83 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 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 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 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 Play Video |
Finding the Height of the Satellite In this video I will find the height of an Earth orbiting satellite. |
Lecture 88 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 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 Play Video |
Find Distance Between Ships In this video I will find the distance between 2 ships traveling in different directions. |
Lecture 94 Play Video |
Heron's Formula: Intro In this video I will introduce Heron's Formula and its applications. |
Lecture 95 Play Video |
Heron's Formula Proved In this video I will prove Heron's Formula. |
X. Trigonometric Identities | |
Lecture 96 Play Video |
What are the basic trigonometric identities? In this video I will introduce the first 3 basic trigonometric identities. |
Lecture 97 Play Video |
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 Play Video |
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 Play Video |
Verify the Identity: 2 In this video I will verify the identity (1+tanx)/(1-tanx)=(cosx+sinx)/(cosx-sinx). |
Lecture 102 Play Video |
Verify the Identity: 3 In this video I will verify the identity (tanx-cotx)/(tan^2x-cot^2x)=sinxcosx. |
Lecture 103 Play Video |
Verify the Identity: 4 In this video I will verify the identity secx/(secx-tanx)=secx(secx+tanx). |
Lecture 104 Play Video |
Addition and Subtraction Formulas In this video I will introduce trigonometric addition and subtraction formulas. |
Lecture 105 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 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 Play Video |
Proving the Cofunction Idenity In this video I will prove the trigonometric cofunction cos[(pi/2)-x]=sinx. |
Lecture 108 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 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 Play Video |
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 Play Video |
Proof Using Addition & Subtraction Formulas In this video I will prove the trigonometric identity tanA-tanB=sin(A-B)/(cosAcosB). |
Lecture 116 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 Play Video |
Double Angle Formula: Introduction In this video I will introduce the double angle formulas sin2A, cos2A, tan2A. |
Lecture 118 Play Video |
Double Angle Formula Proved: Sine In this video I will prove the double angle formula sin2A=2sinAcosA. |
Lecture 119 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 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 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 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 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 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 Play Video |
Proof sin^2(x)=(1-cos2x)/2 In this video I will prove sin^2(x)=(1-cos2x)/2. |
Lecture 126 Play Video |
Proof cos^2(x)=(1+cos2x)/2 In this video I will prove cos^2(x)=(1+cos2x)/2. |
Lecture 127 Play Video |
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 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 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: https://www.youtube.com/watch?v=j60yiSvan8Y 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 Play Video |
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=? |