This lesson first starts with how to test for symmetry in a polar graph. Symmetry to the Polar Axis at 1:34 Symmetry to the line Theta=pi/2 at 8:13 Symmetry to the Pole at 10:38 Special Types of Graphs Circles at 13:13 Limacons at 16:16 I explain how to recognize the 4 subcategories of Limacons which are Inner Loop, Cartiod, Dimpled, and Convex. EXAMPLE of graphing a Limacon with an inner loop at 20:29 Rose Curve introduced at 34:10 EXAMPLE with even number of petals at 38:01 EXAMPLE with odd number of petals at 49:36 Lemniscates introduced at 54:03 LAST EXAMPLE at 55:14Graphing Calculator Example at 26:50My introductory video of Understanding Polar Coordinates www.youtube.com/watch?v=tKi05dfUhAA

1. Standard Position Angles & Radians Part 1
2. Standard Position Angles & Radians Part 2
3. Angle Measures in Degrees Minutes & Seconds DMS
4. Setting up the Unit Circle Part 1 and Reference Angle
5. Setting Up the Unit Circle Part 2
6. Linear & Angular Speed Part 1
7. Linear & Angular Speed Part 2
8. Evaluating Trig Functions w/ Unit Circle Degrees & Radians
9. Fundamental Trigonometric Identities Intro & Proofs
10. Trig Expressions & Finding Trig Functions Given another Trig Ratio
11. Right Triangle Trigonometry Part 1
12. Right Triangle Trigonometry Part 2
13. Trigonometric Cofunctions
14. Trigonometric Functions of Any Angle
15. Understanding Basic Sine & Cosine Graphs
16. Graphing Sine & Cosine w/out a Calculator Pt1
17. Graphing Sine & Cosine w/out a Calculator Pt 2
18. Equation of Sine and Cosine from a Graph
19. Water Depth Word Problem Modeled with Cosine Sine Function
20. Intro Tangent & Cotangent Graphs
21. Tangent & Cotangent Graphs w/ Transformations
22. Graphing Secant & Cosecant w/ t-table
23. Evaluating Inverse Trigonometric Functions
24. Verifying Trigonometric Identities Pt 1
25. Verifying Trigonometric Identities - Part I
26. Verifying Trigonometric Identities - Part II
27. Verifying Trigonometric Identities - Part III
28. Sum and Difference Trigonometric Identities
29. Verifying Trigonometric Identities Involving Sum & Difference
30. Evaluating Trigonometry Expressions with Half and Double Angles Pt1
31. Evaluating Trigonometry Expressions with Half and Double Angles Pt2
32. Trigonometry Proofs Involving Half and Double Angles
33. Trigonometric Equations Single Angle 0 to 2π Restriction
34. Single Angle Trigonometric Equations All Solutions
35. Trigonometric Equations Multiple Angles 0 to 2π Restriction
36. Trigonometric Equations Multiple Angles All Solutions
37. Oblique Triangles Law of Sines
38. Ambiguous Case for Law of Sines
39. Law of Cosines
40. Area of oblique triangles SAS SSS Heron's Formula
41. Applications of Law of Sines and Cosines
42. Understanding Polar Coordinates
43. Converting Coordinates between Polar and Rectangular Form
44. Converting Equations Between Polar & Rectangular Form
45. Graphing Polar Equations, Test for Symmetry & 4 Examples Corrected
46. Complex Numbers in Polar Form
47. Product & Quotient of Polar Complex Numbers
48. De Moivre's Theorem powers of Polar Complex Numbers
49. De Moivre's Theorem Roots of Polar Complex Numbers
50. Introduction to Vectors
51. Writing Vector in terms of Magnitude & Direction Example
52. Vector Application Examples
53. Dot Product & Angle Between Vectors
54. Projection of a Vector onto another Vector
55. Trigonometry Bearing Problems - 4 Examples

In this series, the very helpful and fun math teacher Mr. Tarrou teaches students an entire course on trigonometry from start to finish, and on top of that, provides a comprehensive and easy to understand introduction to polar coordinates, vectors, and complex numbers. His videos are friendly, easy to understand, entertaining, and very well organized, all thanks to Mr. Tarrou great dedication to teaching and enthusiasm for mathematics.