Section 1: Trigonometric Functions 

Angles 
39:05 
 
Intro 
0:00  
 
Degrees 
0:22  
 
 Circle is 360 Degrees 
0:48  
 
 Splitting a Circle 
1:13  
 
Radians 
2:08  
 
 Circle is 2 Pi Radians 
2:31  
 
 One Radian 
2:52  
 
 HalfCircle and Right Angle 
4:00  
 
Converting Between Degrees and Radians 
6:24  
 
 Formulas for Degrees and Radians 
6:52  
 
Coterminal, Complementary, Supplementary Angles 
7:23  
 
 Coterminal Angles 
7:30  
 
 Complementary Angles 
9:40  
 
 Supplementary Angles 
10:08  
 
Example 1: Dividing a Circle 
10:38  
 
Example 2: Converting Between Degrees and Radians 
11:56  
 
Example 3: Quadrants and Coterminal Angles 
14:18  
 
Extra Example 1: Common Angle Conversions 
8:02  
 
Extra Example 2: Quadrants and Coterminal Angles 
7:14  

Sine and Cosine Functions 
43:16 
 
Intro 
0:00  
 
Sine and Cosine 
0:15  
 
 Unit Circle 
0:22  
 
 Coordinates on Unit Circle 
1:03  
 
 Right Triangles 
1:52  
 
 Adjacent, Opposite, Hypotenuse 
2:25  
 
 Master Right Triangle Formula: SOHCAHTOA 
2:48  
 
Odd Functions, Even Functions 
4:40  
 
 Example: Odd Function 
4:56  
 
 Example: Even Function 
7:30  
 
Example 1: Sine and Cosine 
10:27  
 
Example 2: Graphing Sine and Cosine Functions 
14:39  
 
Example 3: Right Triangle 
21:40  
 
Example 4: Odd, Even, or Neither 
26:01  
 
Extra Example 1: Right Triangle 
4:05  
 
Extra Example 2: Graphing Sine and Cosine Functions 
5:23  

Sine and Cosine Values of Special Angles 
33:05 
 
Intro 
0:00  
 
454590 Triangle and 306090 Triangle 
0:08  
 
 454590 Triangle 
0:21  
 
 306090 Triangle 
2:06  
 
Mnemonic: All Students Take Calculus (ASTC) 
5:21  
 
 Using the Unit Circle 
5:59  
 
 New Angles 
6:21  
 
 Other Quadrants 
9:43  
 
 Mnemonic: All Students Take Calculus 
10:13  
 
Example 1: Convert, Quadrant, Sine/Cosine 
13:11  
 
Example 2: Convert, Quadrant, Sine/Cosine 
16:48  
 
Example 3: All Angles and Quadrants 
20:21  
 
Extra Example 1: Convert, Quadrant, Sine/Cosine 
4:15  
 
Extra Example 2: All Angles and Quadrants 
4:03  

Modified Sine Waves: Asin(Bx+C)+D and Acos(Bx+C)+D 
52:03 
 
Intro 
0:00  
 
Amplitude and Period of a Sine Wave 
0:38  
 
 Sine Wave Graph 
0:58  
 
 Amplitude: Distance from Middle to Peak 
1:18  
 
 Peak: Distance from Peak to Peak 
2:41  
 
Phase Shift and Vertical Shift 
4:13  
 
 Phase Shift: Distance Shifted Horizontally 
4:16  
 
 Vertical Shift: Distance Shifted Vertically 
6:48  
 
Example 1: Amplitude/Period/Phase and Vertical Shift 
8:04  
 
Example 2: Amplitude/Period/Phase and Vertical Shift 
17:39  
 
Example 3: Find Sine Wave Given Attributes 
25:23  
 
Extra Example 1: Amplitude/Period/Phase and Vertical Shift 
7:27  
 
Extra Example 2: Find Cosine Wave Given Attributes 
10:27  

Tangent and Cotangent Functions 
36:04 
 
Intro 
0:00  
 
Tangent and Cotangent Definitions 
0:21  
 
 Tangent Definition 
0:25  
 
 Cotangent Definition 
0:47  
 
Master Formula: SOHCAHTOA 
1:01  
 
 Mnemonic 
1:16  
 
Tangent and Cotangent Values 
2:29  
 
 Remember Common Values of Sine and Cosine 
2:46  
 
 90 Degrees Undefined 
4:36  
 
Slope and Mnemonic: ASTC 
5:47  
 
 Uses of Tangent 
5:54  
 
 Example: Tangent of Angle is Slope 
6:09  
 
 Sign of Tangent in Quadrants 
7:49  
 
Example 1: Graph Tangent and Cotangent Functions 
10:42  
 
Example 2: Tangent and Cotangent of Angles 
16:09  
 
Example 3: Odd, Even, or Neither 
18:56  
 
Extra Example 1: Tangent and Cotangent of Angles 
2:27  
 
Extra Example 2: Tangent and Cotangent of Angles 
5:02  

Secant and Cosecant Functions 
27:18 
 
Intro 
0:00  
 
Secant and Cosecant Definitions 
0:17  
 
 Secant Definition 
0:18  
 
 Cosecant Definition 
0:33  
 
Example 1: Graph Secant Function 
0:48  
 
Example 2: Values of Secant and Cosecant 
6:49  
 
Example 3: Odd, Even, or Neither 
12:49  
 
Extra Example 1: Graph of Cosecant Function 
4:58  
 
Extra Example 2: Values of Secant and Cosecant 
5:19  

Inverse Trigonometric Functions 
32:58 
 
Intro 
0:00  
 
Arcsine Function 
0:24  
 
 Restrictions between 1 and 1 
0:43  
 
 Arcsine Notation 
1:26  
 
Arccosine Function 
3:07  
 
 Restrictions between 1 and 1 
3:36  
 
 Cosine Notation 
3:53  
 
Arctangent Function 
4:30  
 
 Between Pi/2 and Pi/2 
4:44  
 
 Tangent Notation 
5:02  
 
Example 1: Domain/Range/Graph of Arcsine 
5:45  
 
Example 2: Arcsin/Arccos/Arctan Values 
10:46  
 
Example 3: Domain/Range/Graph of Arctangent 
17:14  
 
Extra Example 1: Domain/Range/Graph of Arccosine 
4:30  
 
Extra Example 2: Arcsin/Arccos/Arctan Values 
5:40  

Computations of Inverse Trigonometric Functions 
31:08 
 
Intro 
0:00  
 
Inverse Trigonometric Function Domains and Ranges 
0:31  
 
 Arcsine 
0:41  
 
 Arccosine 
1:14  
 
 Arctangent 
1:41  
 
Example 1: Arcsines of Common Values 
2:44  
 
Example 2: Odd, Even, or Neither 
5:57  
 
Example 3: Arccosines of Common Values 
12:24  
 
Extra Example 1: Arctangents of Common Values 
5:50  
 
Extra Example 2: Arcsin/Arccos/Arctan Values 
8:51  
Section 2: Trigonometric Identities 

Pythagorean Identity 
19:11 
 
Intro 
0:00  
 
Pythagorean Identity 
0:17  
 
 Pythagorean Triangle 
0:27  
 
 Pythagorean Identity 
0:45  
 
Example 1: Use Pythagorean Theorem to Prove Pythagorean Identity 
1:14  
 
Example 2: Find Angle Given Cosine and Quadrant 
4:18  
 
Example 3: Verify Trigonometric Identity 
8:00  
 
Extra Example 1: Use Pythagorean Identity to Prove Pythagorean Theorem 
3:32  
 
Extra Example 2: Find Angle Given Cosine and Quadrant 
3:55  

Identity Tan(squared)x+1=Sec(squared)x 
23:16 
 
Intro 
0:00  
 
Main Formulas 
0:19  
 
 Companion to Pythagorean Identity 
0:27  
 
 For Cotangents and Cosecants 
0:52  
 
 How to Remember 
0:58  
 
Example 1: Prove the Identity 
1:40  
 
Example 2: Given Tan Find Sec 
3:42  
 
Example 3: Prove the Identity 
7:45  
 
Extra Example 1: Prove the Identity 
2:22  
 
Extra Example 2: Given Sec Find Tan 
4:34  

Addition and Subtraction Formulas 
52:52 
 
Intro 
0:00  
 
Addition and Subtraction Formulas 
0:09  
 
 How to Remember 
0:48  
 
Cofunction Identities 
1:31  
 
 How to Remember Graphically 
1:44  
 
 Where to Use Cofunction Identities 
2:52  
 
Example 1: Derive the Formula for cos(AB) 
3:08  
 
Example 2: Use Addition and Subtraction Formulas 
16:03  
 
Example 3: Use Addition and Subtraction Formulas to Prove Identity 
25:11  
 
Extra Example 1: Use cos(AB) and Cofunction Identities 
7:54  
 
Extra Example 2: Convert to Radians and use Formulas 
11:32  

Double Angle Formulas 
29:05 
 
Intro 
0:00  
 
Main Formula 
0:07  
 
 How to Remember from Addition Formula 
0:18  
 
 Two Other Forms 
1:35  
 
Example 1: Find Sine and Cosine of Angle using Double Angle 
3:16  
 
Example 2: Prove Trigonometric Identity using Double Angle 
9:37  
 
Example 3: Use Addition and Subtraction Formulas 
12:38  
 
Extra Example 1: Find Sine and Cosine of Angle using Double Angle 
6:10  
 
Extra Example 2: Prove Trigonometric Identity using Double Angle 
3:18  

HalfAngle Formulas 
43:55 
 
Intro 
0:00  
 
Main Formulas 
0:09  
 
 Confusing Part 
0:34  
 
Example 1: Find Sine and Cosine of Angle using HalfAngle 
0:54  
 
Example 2: Prove Trigonometric Identity using HalfAngle 
11:51  
 
Example 3: Prove the HalfAngle Formula for Tangents 
18:39  
 
Extra Example 1: Find Sine and Cosine of Angle using HalfAngle 
7:16  
 
Extra Example 2: Prove Trigonometric Identity using HalfAngle 
3:34  
Section 3: Applications of Trigonometry 

Trigonometry in Right Angles 
25:43 
 
Intro 
0:00  
 
Master Formula for Right Angles 
0:11  
 
 SOHCAHTOA 
0:15  
 
 Only for Right Triangles 
1:26  
 
Example 1: Find All Angles in a Triangle 
2:19  
 
Example 2: Find Lengths of All Sides of Triangle 
7:39  
 
Example 3: Find All Angles in a Triangle 
11:00  
 
Extra Example 1: Find All Angles in a Triangle 
5:10  
 
Extra Example 2: Find Lengths of All Sides of Triangle 
4:18  

Law of Sines 
56:40 
 
Intro 
0:00  
 
Law of Sines Formula 
0:18  
 
 SOHCAHTOA 
0:27  
 
 Any Triangle 
0:59  
 
 Graphical Representation 
1:25  
 
 Solving Triangle Completely 
2:37  
 
When to Use Law of Sines 
2:55  
 
 ASA, SAA, SSA, AAA 
2:59  
 
 SAS, SSS for Law of Cosines 
7:11  
 
Example 1: How Many Triangles Satisfy Conditions, Solve Completely 
8:44  
 
Example 2: How Many Triangles Satisfy Conditions, Solve Completely 
15:30  
 
Example 3: How Many Triangles Satisfy Conditions, Solve Completely 
28:32  
 
Extra Example 1: How Many Triangles Satisfy Conditions, Solve Completely 
8:01  
 
Extra Example 2: How Many Triangles Satisfy Conditions, Solve Completely 
15:11  

Law of Cosines 
49:05 
 
Intro 
0:00  
 
Law of Cosines Formula 
0:23  
 
 Graphical Representation 
0:34  
 
 Relates Sides to Angles 
1:00  
 
 Any Triangle 
1:20  
 
 Generalization of Pythagorean Theorem 
1:32  
 
When to Use Law of Cosines 
2:26  
 
 SAS, SSS 
2:30  
 
Heron's Formula 
4:49  
 
 Semiperimeter S 
5:11  
 
Example 1: How Many Triangles Satisfy Conditions, Solve Completely 
5:53  
 
Example 2: How Many Triangles Satisfy Conditions, Solve Completely 
15:19  
 
Example 3: Find Area of a Triangle Given All Side Lengths 
26:33  
 
Extra Example 1: How Many Triangles Satisfy Conditions, Solve Completely 
11:05  
 
Extra Example 2: Length of Third Side and Area of Triangle 
9:17  

Finding the Area of a Triangle 
27:37 
 
Intro 
0:00  
 
Master Right Triangle Formula and Law of Cosines 
0:19  
 
 SOHCAHTOA 
0:27  
 
 Law of Cosines 
1:23  
 
Heron's Formula 
2:22  
 
 Semiperimeter S 
2:37  
 
Example 1: Area of Triangle with Two Sides and One Angle 
3:12  
 
Example 2: Area of Triangle with Three Sides 
6:11  
 
Example 3: Area of Triangle with Three Sides, No Heron's Formula 
8:50  
 
Extra Example 1: Area of Triangle with Two Sides and One Angle 
2:54  
 
Extra Example 2: Area of Triangle with Two Sides and One Angle 
6:48  

Word Problems and Applications of Trigonometry 
34:25 
 
Intro 
0:00  
 
Formulas to Remember 
0:11  
 
 SOHCAHTOA 
0:15  
 
 Law of Sines 
0:55  
 
 Law of Cosines 
1:48  
 
 Heron's Formula 
2:46  
 
Example 1: Telephone Pole Height 
4:01  
 
Example 2: Bridge Length 
7:48  
 
Example 3: Area of Triangular Field 
14:20  
 
Extra Example 1: Kite Height 
4:36  
 
Extra Example 2: Roads to a Town 
10:34  

Vectors 
46:42 
 
Intro 
0:00  
 
Vector Formulas and Concepts 
0:12  
 
 Vectors as Arrows 
0:28  
 
 Magnitude 
0:38  
 
 Direction 
0:50  
 
 Drawing Vectors 
1:16  
 
 Uses of Vectors: Velocity, Force 
1:37  
 
 Vector Magnitude Formula 
3:15  
 
 Vector Direction Formula 
3:28  
 
 Vector Components 
6:27  
 
Example 1: Magnitude and Direction of Vector 
8:00  
 
Example 2: Force to a Box on a Ramp 
12:25  
 
Example 3: Plane with Wind 
18:30  
 
Extra Example 1: Components of a Vector 
2:54  
 
Extra Example 2: Ship with a Current 
13:13  
Section 4: Complex Numbers and Polar Coordinates 

Polar Coordinates 
1:07:35 
 
Intro 
0:00  
 
Polar Coordinates vs Rectangular/Cartesian Coordinates 
0:12  
 
 Rectangular Coordinates, Cartesian Coordinates 
0:23  
 
 Polar Coordinates 
0:59  
 
Converting Between Polar and Rectangular Coordinates 
2:06  
 
 R 
2:16  
 
 Theta 
2:48  
 
Example 1: Convert Rectangular to Polar Coordinates 
6:53  
 
Example 2: Convert Polar to Rectangular Coordinates 
17:28  
 
Example 3: Graph the Polar Equation 
28:00  
 
Extra Example 1: Convert Polar to Rectangular Coordinates 
10:01  
 
Extra Example 2: Graph the Polar Equation 
10:53  

Complex Numbers 
35:59 
 
Intro 
0:00  
 
Main Definition 
0:07  
 
 Number i 
0:23  
 
 Complex Number Form 
0:33  
 
Powers of Imaginary Number i 
1:00  
 
 Repeating Pattern 
1:43  
 
Operations on Complex Numbers 
3:30  
 
 Adding and Subtracting Complex Numbers 
3:39  
 
 Multiplying Complex Numbers 
4:39  
 
 FOIL Method 
5:06  
 
 Conjugation 
6:29  
 
Dividing Complex Numbers 
7:34  
 
 Conjugate of Denominator 
7:45  
 
Example 1: Solve For Complex Number z 
11:02  
 
Example 2: Expand and Simplify 
15:34  
 
Example 3: Simplify the Powers of i 
17:50  
 
Extra Example 1: Simplify 
4:37  
 
Extra Example 2: All Complex Numbers Satisfying Equation 
10:00  

Polar Form of Complex Numbers 
40:43 
 
Intro 
0:00  
 
Polar Coordinates 
0:49  
 
 Rectangular Form 
0:52  
 
 Polar Form 
1:25  
 
 R and Theta 
1:51  
 
Polar Form Conversion 
2:27  
 
 R and Theta 
2:35  
 
 Optimal Values 
4:05  
 
 Euler's Formula 
4:25  
 
Multiplying Two Complex Numbers in Polar Form 
6:10  
 
 Multiply r's Together and Add Exponents 
6:32  
 
Example 1: Convert Rectangular to Polar Form 
7:17  
 
Example 2: Convert Polar to Rectangular Form 
13:49  
 
Example 3: Multiply Two Complex Numbers 
17:28  
 
Extra Example 1: Convert Between Rectangular and Polar Forms 
6:48  
 
Extra Example 2: Simplify Expression to Polar Form 
7:48  

DeMoivre's Theorem 
57:37 
 
Intro 
0:00  
 
Introduction to DeMoivre's Theorem 
0:10  
 
 n nth Roots 
3:06  
 
DeMoivre's Theorem: Finding nth Roots 
3:52  
 
 Relation to Unit Circle 
6:29  
 
 One nth Root for Each Value of k 
7:11  
 
Example 1: Convert to Polar Form and Use DeMoivre's Theorem 
8:24  
 
Example 2: Find Complex Eighth Roots 
15:27  
 
Example 3: Find Complex Roots 
27:49  
 
Extra Example 1: Convert to Polar Form and Use DeMoivre's Theorem 
7:41  
 
Extra Example 2: Find Complex Fourth Roots 
14:36  