  # Pre-Calculus 6-9: Trigonometry Review

### Course Description Michel van Biezen teaching trigonometric identities
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### Video Lectures & Study Materials

# Lecture Play Lecture
I. The Unit Circle
1 What Is The Unit Circle? Play Video
2 The Unit Circle and The Angle (Part 1 of 2) Play Video
3 The Unit Circle and The Angle (Part 2 of 2) Play Video
4 The Unit Circle and The Angle (30 and 60 Degrees) Play Video
5 The Unit Circle and The Signs of x and y Play Video
II. Trigonometric Functions
6 The Trigonometry Function: Sine Explained Play Video
7 The Trigonometry Function: Cosine Explained Play Video
8 The Trigonometry Function: Tanget Explained Play Video
9 The Trigonometry Function: Cotanget Explained Play Video
10 The Trigonometry Function: Secant Explained Play Video
11 The Trigonometry Function: Cosecant Explained Play Video
III. Trigonometric Angles
12 What Are Negative Angles? Play Video
13 How to Convert Angles Greater Than 360? Play Video
14 What Are Odd and Even Functions? Play Video
15 Fundamental Trig Idenities Play Video
16 Using the Unit Circle to Evaluate Trig Functions Play Video
17 Using the Unit Circle to Evaluate Trig Functions Play Video
18 Using the Unit Circle to Evaluate Trig Functions Play Video
IV. Reduction Formulas
19 Reduction Formula (1 of 4) Add/Subtract 2pi Play Video
20 Reduction Formula (2 of 4) Add/Subtract pi Play Video
21 Reduction Formula (3 of 4) Add pi/2 Play Video
22 Reduction Formula (4 of 4) Subtract pi/2 Play Video
V. Graphing Trigonometric Functions
23 Graphing y=sin(theta) (1 of 2) Play Video
24 Graphing y=sin(theta) (2 of 2) And the Unit Circle Play Video
25 Graphing y=cos(theta) Play Video
26 Graphing y=tan(theta) Play Video
27 Period of the Sine and Cosine Graphs Play Video
28 The General Equation for Sine and Cosine Play Video
29 The General Equation for Sine and Cosine: Amplitude Play Video
30 The General Equation for Sine and Cosine: Period Play Video
31 The General Equation for Sine and Cosine: Left/Right Shift Play Video
32 The General Equation for Sine and Cosine: Up/Down Shift Play Video
33 Graphing Sum of Trigonometry Functions (1 of 2) Play Video
34 Graphing Sum of Trigonometry Functions (2 of 2) Play Video
35 Graphing the Negative of a Trig Function Play Video
36 Graphing the Product of a Trig Function (No Calculators!) Play Video
37 Graphing the Product of a Trig Function (No Calculators!) Play Video
38 Graphing the Product of a Trig Function (No Calculators!) Play Video
39 Graph the Function y=-(1/2)sinx Play Video
40 Graph the Function y=2+2cosx Play Video
41 Find the Amplitude, Period, and Graph y=-3sin3x Play Video
42 Find the Amplitude, Period, and Graph y=4cos[(1/2)x] Play Video
43 Find the Amplitude, Period, and Graph y=cos[x-(pi/2)] Play Video
44 Find the Amplitude, Period, and Graph y=3sin[(2x/3)-(pi/6)] Play Video
45 Find the Amplitude, Period, and Graph y=2cos[3x+(pi/4)]-1 Play Video
46 Find the Amplitude, Period, Phase Angle, and Write Equation Play Video
47 Find the Amplitude, Period, Phase Angle, and Write Equation Play Video
48 Find the Amplitude, Period, Phase Angle, and Write Equation Play Video
49 Graph y=tan4x Play Video
50 Graph y=csc2x Play Video
VI. Inverse Trigonometric Functions
51 Inverse Sine Function Play Video
52 Inverse Cosine Function Play Video
53 Inverse Tangent Function Play Video
54 Inverse Trigonometric Function: Don't Get Confused! Play Video
VII. The Right Triangle
55 Angle In Radians Play Video
56 Length of Arc (Circumference) Play Video
57 Area of Sector (Circle) Play Video
58 Basics of Trigonometry Play Video
59 Basics of Trigonometry: Example Play Video
60 Basics of Trigonometry: Exercise 1 Play Video
61 Basics of Trigonometry: Exercise 2 Play Video
62 Basics of Trigonometry: Exercise 3 Play Video
63 Basics of Trigonometry: Exercise 4 Play Video
64 Inverse Trig Functions: Find Angle Play Video
65 Inverse Trig Functions: Ex. 1 Play Video
66 Inverse Trig Functions: Ex. 2 Play Video
67 Inverse Trig Functions: Summary Play Video
68 Find All Unknowns (Adj=? Opp=?) Play Video
69 Find All Unknowns (Adj=? Hyp=?) Play Video
70 Find All Unknowns (Adj=? Angle=?) Play Video
71 Challenge Problem #1 Play Video
72 Challenge Problem #2 Play Video
73 Challenge Problem #3 Play Video
74 Challenge Problem #4 Play Video
75 Height of Flag = ? Play Video
76 Distance to Near-By Star = ? Play Video
77 Height of Building = ? Play Video
78 Distance Between Venus & Sun = ? Play Video
79 Circumference of the Planet = ? Play Video
80 Angle of Geosynchronous Satellite = ? Play Video
VIII. The Law of Sines
81 Definition of The Law of Sines Play Video
82 The Law of Sines Proved Play Video
83 Example of SSA (Side-Side-Angle) Play Video
84 Example of AAS (Angle-Angle-Side) Play Video
85 Caution: NO Solution cases with Law of Sines Play Video
86 Multiple Solutions with Law of Sines Play Video
87 Finding the Height of the Satellite Play Video
88 Finding the Height of the Mountain Play Video
IX. The Law of Cosines
89 What is the Law of Cosines? Play Video
90 Finding 3 Angles Given 3 Sides Play Video
91 The Law of Cosines Proved Play Video
92 Find Distance and Bearing of Airplane Play Video
93 Find Distance Between Ships Play Video
94 Heron's Formula: Intro Play Video
95 Heron's Formula Proved Play Video
X. Trigonometric Identities
96 What are the basic trigonometric identities? Play Video
97 Cofunction Trigonometric Identities Play Video
98 Simplify the Trig Expression: 1 Play Video
99 Simplify the Trig Expression: 2 Play Video
100 Verify the Identity: 1 Play Video
101 Verify the Identity: 2 Play Video
102 Verify the Identity: 3 Play Video
103 Verify the Identity: 4 Play Video
104 Addition and Subtraction Formulas Play Video
105 Proof of Addition Formula (Cosine) Play Video
106 Proof of Subtraction Formula (Cosine) Play Video
107 Proving the Cofunction Idenity Play Video
108 Proof of Addition Formula (Sine) Play Video
109 Proof of Subtraction Formula (Sine) Play Video
110 Proof of the Addition Formula (Tangent) Play Video
111 Proof of the Subtraction Formula (Tangent) Play Video
112 Find sin75,...tan135 (Without a Calculator) Play Video
113 Proof Using Addition & Subtraction Formulas Play Video
114 Proof Using Addition & Subtraction Formulas Play Video
115 Proof Using Addition & Subtraction Formulas Play Video
116 Proof Using Addition & Subtraction Formulas Play Video
117 Double Angle Formula: Introduction Play Video
118 Double Angle Formula Proved: Sine Play Video
119 Double Angle Formula Proved: Cosine Play Video
120 Double Angle Formula Proved: Tangent Play Video
121 Simplifying Triple Angles to a Single Angle Play Video
122 Formula for Lowering Power cos^2(x)=? Play Video
123 Formula for Lowering Power sin^2(x)=? Play Video
124 Formula for Lowering Power tan^2(x)=? Play Video
125 Proof sin^2(x)=(1-cos2x)/2 Play Video
126 Proof cos^2(x)=(1+cos2x)/2 Play Video
127 Proof Half Angle Formula: sin(x/2) Play Video
128 Proof Half Angle Formula: cos(x/2) Play Video
129 Proof Half Angle Formula: tan(x/2) Play Video
130 Product to Sum Formula 1 Play Video
131 Product to Sum Formula 2 Play Video
132 Sum to Product Formula 1 Play Video
133 Sum to Product Formula 2 Play Video
134 Write sin(2x)cos3x as a Sum Play Video
135 Write cos4x-cos6x as a Product Play Video
136 Prove cos^4(x)-sin^4(x)=cos2x Play Video
137 Prove [sinx+sin(5x)]/[cosx+cos(5x)]=tan3x Play Video
138 Prove (sinA+sinB)/(cosA+cosB)=tan[(A+B)/2] Play Video
139 Prove sin(4x)/sinx=4cosxcos(2x) Play Video
140 Solve cos(theta)+1=0, theta=? Play Video
141 Solve 3sin(theta)-1=0, theta=? Play Video
142 Solve tan^2(theta)-4=0, theta=? Play Video
143 Solve 2sin^2(theta)-sin(theta)-1=0, theta=? Play Video
144 Solve 2cos^2(theta)-7cos(theta)+3=0, theta=? Play Video
145 Solve cos(x)sin(x)-2cos(x)=0, x=? Play Video
146 Solve 3tan(x)sin(x)-2tan(x)=0, x=? Play Video
147 Solve 3tan^3(theta)=tan(theta), theta=? Play Video
148 Solve sin(2theta)+cos(theta)=0, theta=? Play Video
149 Solve sin(theta)+sin(3theta)=0, theta=? Play Video
150 Solve 2cos(3theta)=1, theta=? Play Video
151 Solve sin(2theta)=3cos(2theta), theta=? Play Video
152 Solve 2sin(x)tan(x)-tan(x)=1-2sin(x), x=? Play Video