I work through 5 examples of application of vectors. NOTE: In the last example I state the wind speed is 27 mph, but then use a wind speed of 10 mph in my problem. I added annotations over the written example but you will not see this on your iPad or iPhone.The angle Theta in the work formula of the first example is "The difference between the angle the force is being applied and the direction of the work."Because I am just a math teacher and not a science teacher, I learned something from a viewer/teacher I am guessing. Here is there reply...59ejf I liked your video.However, a couple of comments are warranted. First: Force and energy are not the same thing and should not be used interchangeably. In fact, the vertical component of the force exerted on the handle of your wagon imparts no energy on the wagon. In fact, it doesn't even do any work on the wagon. Thus there is NO waste of energy.Second: This gets complicated. For instance, if a person is holding a couple of five pound buckets away from her body, she will soon tire and have to quit holding them up.She is not doing any work on the buckets by holding them up, as work is force times distance. If the buckets don't move, no distance is travelled by the forces and no work is done. She is exerting a force, but the forces are static. Energy and work have the same units. If no work is done, no energy is expended. Yet if you ask her if she did any work, she will say duh, to exhaustion.Be careful with using humans in your physics problems.

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.