  # Trigonometry & Complex Numbers

### Course Description

Patrick providers a full course with more than 150 video lectures covering everything from angles and trigonometry, to polar coordinates and complex numbers. Lecture 46: Finding a Formula for a Trigonometric Graph, Ex 1
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### Video Lectures & Study Materials

# Lecture Play Lecture
I. Angles and Arc Length
1 Finding the Quadrant in Which an Angle Lies - Example 1 (6:16) Play Video
2 Finding the Quadrant in Which an Angle Lies - Example 2 (4:54) Play Video
3 Finding the Quadrant in Which an Angle Lies - Example 3 (3:13) Play Video
4 Coterminal Angles - Example 1 (7:15) Play Video
5 Coterminal Angles - Example 2 (3:27) Play Video
6 Complementary and Supplementary Angles - Example 1 (4:01) Play Video
7 Complementary and Supplementary Angles - Example 2 (4:11) Play Video
8 Degrees and Radians and Converting Between Them! Example 1 (5:57) Play Video
9 Arc Length Formula - Example 1 (5:20) Play Video
10 Arc Length Formula - Example 2 (3:19) Play Video
II. Trigonometric Functions
11 Finding Trigonometric Function Values Given One Trig Value in a Right Triangle, Ex 1 (6:24) Play Video
12 Finding Trigonometric Function Values Given One Trig Value in a Right Triangle, Ex 2 (5:24) Play Video
13 Finding Trigonometric Function Values Given One Trig Value in a Right Triangle, Ex 3 (2:09) Play Video
14 Finding an Angle Given the Value of a Trigonometric Function - Example 1 (3:46) Play Video
15 Finding an Angle Given the Value of a Trigonometric Function - Example 2 (1:58) Play Video
16 Trigonometric Functions To Find Unknown Sides of Right Triangles, Ex 1 (5:25) Play Video
17 Trigonometric Functions To Find Unknown Sides of Right Triangles, Ex 2 (3:11) Play Video
18 Trigonometric Functions To Find Unknown Sides of Right Triangles, Ex 3 (2:36) Play Video
19 Finding the Height of an Object Using Trigonometry, Example 1 (3:32) Play Video
20 Finding the Height of an Object Using Trigonometry, Example 2 (2:17) Play Video
21 Finding the Height of an Object Using Trigonometry, Example 3 (2:53) Play Video
22 Degrees and Radians (11:59) Play Video
23 A Way to remember the Entire Unit Circle for Trigonometry (7:19) Play Video
24 A Trick to Remember Values on The Unit Circle (4:32) Play Video
25 Evaluating Trigonometric Functions for an Unknown Angle, Given a Point on the Angle, Ex 1 (2:57) Play Video
26 Evaluating Trigonometric Functions for an Unknown Angle, Given a Point on the Angle, Ex 2 (4:01) Play Video
27 Reference Angle for an Angle, Ex 1 (Using Degrees) (5:45) Play Video
28 Reference Angle for an Angle, Ex 2 (Using Radians) (7:12) Play Video
29 Evaluating Trigonometric Functions Using the Reference Angle, Example 1 (7:47) Play Video
30 Evaluating Trigonometric Functions Using the Reference Angle, Example 2 (6:29) Play Video
31 Finding Trigonometric Values Given One Trigonometric Value/Other Info, Example 1 (3:04) Play Video
32 Finding Trigonometric Values Given One Trigonometric Value/Other Info, Example 2 (4:49) Play Video
33 Evaluating Trigonometric Functions at Important Angles, Ex 1 (9:49) Play Video
34 Evaluating Trigonometric Functions at Important Angles, Ex 2 (5:38) Play Video
III. Graphing Trigonometric Functions
35 The Graph of Cosine, y = cos (x) (9:58) Play Video
36 Graphing Sine and Cosine With Different Coefficients (Amplitude and Period), Ex 1 (3:04) Play Video
37 Graphing y = -2 cos(2x) (5:00) Play Video
38 Maximum and Minimum Values of Sine and Cosine Functions, Ex 1 (3:34) Play Video
39 Maximum and Minimum Values of Sine and Cosine Functions, Ex 2 (7:49) Play Video
40 Graphing Sine and Cosine with Phase (Horizontal) Shifts, Example 1 (3:25) Play Video
41 Graphing Sine and Cosine with Phase (Horizontal) Shifts, Example 2 (6:21) Play Video
42 Trigonometric Functions and Graphing: Amplitude, Period, Vertical and Horizontal Shifts, Ex 2 (4:50) Play Video
43 Basic Questions Related to Tangent, Cotangent, Secant, Cosecant, Ex 1 (4:17) Play Video
44 Basic Questions Related to Tangent, Cotangent, Secant, Cosecant, Ex 2 (4:33) Play Video
45 Basic Questions Related to Tangent, Cotangent, Secant, Cosecant, Ex 4 (8:10) Play Video
46 Finding a Formula for a Trigonometric Graph, Ex 1 (4:23) Play Video
47 Finding a Formula for a Trigonometric Graph, Ex 2 (3:01) Play Video
48 Trigonometry Word Problem, Finding The Height of a Building, Example 1 (7:31) Play Video
49 Trigonometry Word Problem, Example 2 (2:13) Play Video
50 Trigonometry Word Problem, Determining the Speed of a Boat, Example 3 (8:28) Play Video
IV. Simplifying Trigonometric Expressions
51 Simplifying Trigonometric Expressions Using Identities, Example 1 (1:05) Play Video
52 Simplifying Trigonometric Expressions Using Identities, Example 2 (3:23) Play Video
53 Simplifying Trigonometric Expressions Using Identities, Example 3 (3:29) Play Video
54 Simplifying Trigonometric Expressions Involving Fractions, Ex 1 (3:47) Play Video
55 Simplifying Trigonometric Expressions Involving Fractions, Example 2 (8:05) Play Video
56 Simplifying Products of Binomials Involving Trigonometric Functions, Ex 1 (3:24) Play Video
57 Simplifying Products of Binomials Involving Trigonometric Functions, Ex 2 (3:41) Play Video
58 Factoring Trigonometric Expressions, Example 1 (3:46) Play Video
59 Factoring and Simplifying Trigonometric Expressions - Example 2 (2:12) Play Video
V. Even and Odd Functions
60 Examples with Trigonometric Functions: Even, Odd or Neither, Example 1 (5:40) Play Video
61 Examples with Trigonometric Functions: Even, Odd or Neither, Example 2 (2:18) Play Video
62 Examples with Trigonometric Functions: Even, Odd or Neither, Example 3 (2:11) Play Video
63 Even, Odd or Neither, Trigonometric Functions, Example 4 (2:07) Play Video
64 Proving an Identity, Example 1 (3:35) Play Video
65 Proving an Identity, Example 2 (5:12) Play Video
66 Proving an Identity - Other Examples, Example 1 (2:30) Play Video
67 Proving an Identity - Other Examples, Example 2 (1:34) Play Video
68 Solving a Basic Trigonometric Equation, Example 1 (2:28) Play Video
69 Solving a Basic Trigonometric Equation, Example 2 (5:00) Play Video
70 Solving a Basic Trigonometric Equation, Example 3 (2:37) Play Video
71 Solve Trigonometric Equation by Factoring, Example 1 (3:02) Play Video
72 Solving a Trigonometric Equation by Factoring, Example 2 (2:55) Play Video
73 Solving a Trigonometric Equation by Factoring, Example 3 (2:11) Play Video
74 Solving Trigonometric Equation, Harder Example - Example 1 (8:56) Play Video
75 Solving Trigonometric Equation, Harder Example - Example 2 (7:07) Play Video
76 Solving Trigonometric Equation , Harder Exampe - Example 3 (3:03) Play Video
77 Solving Trigonometric Equations Using the Quadratic Formula - Example 1 (3:57) Play Video
78 Solving Trigonometric Equations Using the Quadratic Formula - Example 2 (8:46) Play Video
79 Solving Trigonometric Equations Using the Quadratic Formula - Example 3 (11:07) Play Video
80 Solving Word Problems Involving Trigonometric Equations, Example 1 (9:20) Play Video
81 Solving Word Problems Involving Trigonometric Equations, Example 2 (11:35) Play Video
VI. Sum and Difference Trig Identities
82 Identities for Sum and Differences of Sine and Cosine, Example 1 (3:15) Play Video
83 Identities for Sum and Differences of Sine and Cosine, Example 2 (1:57) Play Video
84 Identities for Sum and Differences of Sine and Cosine, Example 3 (6:09) Play Video
85 Sum and Difference Identities for Sine and Cosine, More Examples #1 (2:44) Play Video
86 Sum and Difference Identities for Sine and Cosine, More Examples #2 (2:40) Play Video
87 Sum and Difference Identities for Sine and Cosine, More Examples #3 (8:18) Play Video
88 Sum and Difference Identities to Simplify an Expression, Example 1 (1:13) Play Video
89 Sum and Difference Identities to Simplify an Expression, Example 2 (1:48) Play Video
90 Sum and Difference Identities to Simplify an Expression, Example 3 (1:46) Play Video
91 Using the Sum and Difference Identities for Sine, Cosine and Tangent, Ex 1 (5:17) Play Video
92 Using the Sum and Difference Identities for Sine, Cosine and Tangent, Ex 2 (3:14) Play Video
93 Using the Sum and Difference Identities for Sine, Cosine and Tangent, Ex 3 (2:31) Play Video
VII. Double Angle Trig Identities
94 Using Double Angle Identities to Solve Equations, Example 1 (7:25) Play Video
95 Using Double Angle Identities to Solve Equations, Example 2 (2:12) Play Video
96 Using Double Angle Identities to Solve Equations, Example 3 (3:14) Play Video
97 Word Problems Involving Multiple Angle Identities, Example 1 (5:43) Play Video
98 Word Problems Involving Multiple Angle Identities, Example 2 (4:53) Play Video
99 Word Problems Involving Multiple Angle Identities, Example 3 (2:07) Play Video
100 Cofunction Identities, Example 2 (2:36) Play Video
101 Cofunction Identities, Example 3 (:54) Play Video
102 Power Reducing Formulas for Sine and Cosine, Example 1 (6:02) Play Video
103 Power Reducing Formulas for Sine and Cosine, Example 2 (5:57) Play Video
104 Half Angle Identities to Evaluate Trigonometric Expressions, Example 1 (2:37) Play Video
105 Half Angle Identities to Evaluate Trigonometric Expressions, Example 2 (2:40) Play Video
106 Half Angle Identities to Evaluate Trigonometric Expressions, Example 3 (2:18) Play Video
VIII. Law of Sines
107 The Law of Sines, Example 1 (3:55) Play Video
108 The Law of Sines, Example 2 (3:23) Play Video
109 Law of Sines, Example 3 (6:22) Play Video
110 Side Angle Side for Triangles, Finding Missing Sides/Angles, Example 1 (5:23) Play Video
111 Side Angle Side for Triangles, Finding Missing Sides/Angles, Example 2 (3:28) Play Video
112 Solving a Triangle, SSA, Example 1 (5:25) Play Video
113 Solving a Triangle, SSA, Example 2 (5:11) Play Video
114 Law of Sines - Application/Word Problem, Ex 1 (2:47) Play Video
115 Law of Sines - Application / Word Problem, Ex 2 (7:58) Play Video
116 Law of Sines - Application/Word Problem, Ex 3 (6:27) Play Video
117 Heron's Formula, Example 1 (5:06) Play Video
118 Heron's Formula, Ex 2 (4:00) Play Video
119 Heron's Formula, Example 3 (8:06) Play Video
IX. Law of Cosines
120 Law of Cosines, Example 1 (5:06) Play Video
121 Law of Cosines, Example 2 (4:26) Play Video
122 Law of Cosines, Example 3 (2:43) Play Video
123 Law of Cosines, Example 4 (4:27) Play Video
124 Law of Cosines, Example 5 (2:06) Play Video
125 Law of Cosines, Example 6 (3:48) Play Video
126 Law of Cosines, Word Problem #1 (4:03) Play Video
X. Vectors
127 An Introduction to Vectors, Part 1 (4:46) Play Video
128 When Are Two Vectors Considered to Be the Same? (2:03) Play Video
129 Magnitude and Direction of a Vector, Example 1 (3:58) Play Video
130 Magnitude and Direction of a Vector, Example 2 (3:46) Play Video
131 Magnitude and Direction of a Vector, Example 3 (6:05) Play Video
132 Vector Addition and Scalar Multiplication, Example 1 (3:24) Play Video
133 Vector Addition and Scalar Multiplication, Example 2 (3:52) Play Video
134 Finding the Components of a Vector, Ex 1 (2:38) Play Video
135 Finding the Components of a Vector, Ex 2 (6:34) Play Video
136 Finding a Unit Vector, Ex 1 (2:07) Play Video
137 Finding a Unit Vector, Ex 2 (4:55) Play Video
138 Word Problems Involving Velocity or Other Forces (Vectors), Ex 1 (3:10) Play Video
139 Word Problems Involving Velocity or Other Forces (Vectors), Ex 2 (11:29) Play Video
140 Word Problems Involving Velocity or Other Forces (Vectors), Ex 3. (2:10) Play Video
XI. Complex Numbers & Trigonometry
141 Complex Numbers: Graphing and Finding the Modulus, Ex 1 (3:40) Play Video
142 Complex Numbers: Graphing and Finding the Modulus, Ex 2 (3:51) Play Video
143 Expressing a Complex Number in Trigonometric or Polar Form, Ex 1 (3:31) Play Video
144 Expressing a Complex Number in Trigonometric or Polar Form, Ex 2 (2:04) Play Video
145 Expressing a Complex Number in Trigonometric or Polar Form, Ex 3 (4:38) Play Video
146 Complex Numbers: Convert From Polar to Complex Form, Ex 1 (2:18) Play Video
147 Complex Numbers: Multiplying and Dividing in Polar Form, Ex 1 (3:27) Play Video
148 Complex Numbers: Multiplying and Dividing in Polar Form, Ex 2 (3:17) Play Video
149 DeMoivre's Theorem: Raising a Complex Number to a Power, Ex 1 (2:18) Play Video
150 DeMoivre's Theorem: Raising a Complex Number to a Power, Ex 2 (11:48) Play Video
151 DeMoivre's Theorem: Raising a Complex Number to a Power, Ex 3 (4:16) Play Video
152 Roots of Complex Numbers, Ex 1 (6:01) Play Video
153 Roots of Complex Numbers, Ex 2 (6:22) Play Video
154 Roots of Complex Numbers, Ex 3 (8:19) Play Video
155 More Roots of Complex Numbers, Ex 1 (9:47) Play Video
156 More Roots of Complex Numbers, Ex 2 (9:43) Play Video
157 Roots of Unity, Example 1 (3:19) Play Video
158 Roots of Unity, Ex 2 (5:48) Play Video
XII. Polar Coordinates
159 Intro to Polar Coordinates, Ex 1 (3:49) Play Video
160 Converting Between Polar and Rectangular (Cartesian) Coordinates, Ex 3 (4:18) Play Video
161 Converting Between Polar and Rectangular Equations, Ex 1 (1:48) Play Video
162 Converting Between Polar and Rectangular Equations, Ex 2 (4:48) Play Video
163 Converting Between Polar and Rectangular Equations, Ex 3 (4:26) Play Video
164 Graphing Simple Polar Equations, Ex 1 (2:30) Play Video
165 Graphing Simple Polar Equations, Ex 2 (3:26) Play Video
166 Graphing Special Polar Equations, Ex 1 (2:06) Play Video
167 Graphing Special Polar Equations; How Many Petals Will a Graph Have? (1:51) Play Video
168 Basic Info About a Limacon (2:27) Play Video