Trigonometry · 40 lessons

Two triangles with the same angles have sides in the same proportion, whatever their size. So once an angle is fixed, the ratio of any two sides is fixed too, and that ratio can be looked up instead of measured. Sine, cosine and tangent are the names of three such ratios.

1. 1The Eight-Point Compass
2. 2Three-Figure Bearings
3. 3Back Bearings
4. Compass Directions and Bearings (11)
5. 4Sine, Cosine and Tangent
6. 5Exact Sine, Cosine and Tangent at 30, 45 and 60°
7. 6Sine and Cosine of Complementary Angles
8. 7Solving Right Triangles
9. 8Finding an Angle from a Ratio
10. 9Elevation and Depression
11. 10Sine and Cosine of Angles Past 90 Degrees
12. 11The Graphs of Sine and Cosine
13. 12The Graph of Tangent
14. 13Amplitude and the Principal Axis
15. 14The Period and Phase Shift of a Wave
16. 15Solving Simple Trigonometric Equations
17. 16The Principal Values of the Inverse Functions
18. 17Quadratic Equations in Sine, Cosine or Tangent
19. 18Trigonometric Equations with a Multiple Angle
20. 19Modeling Tides and Daylight with a Sine Function
21. 20Area with Sine
22. 21The Sine Rule
23. 22The Cosine Rule
24. 23Finding Angles with the Sine Rule
25. 24The Ambiguous Case of the Sine Rule
26. 25Finding Angles with the Cosine Rule
27. 26Trigonometry in Three Dimensions
28. 27Exact Trigonometric Ratios with Surds
29. 28Bearings with the Sine and Cosine Rules
30. Triangle Trigonometry (17)
31. 29Radians
32. 30Exact Trigonometric Values in Radians
33. 31Arc Length and Sector Area
34. 32Trigonometric Identities
35. 33Proving a Trigonometric Identity
36. 34The Compound Angle Formulas
37. 35The Double Angle Formulas
38. 36Secant, Cosecant and Cotangent
39. 37The Identity 1 + tan²θ = sec²θ
40. 38The Harmonic Form R sin(x + α)
41. 39Solving a sin x + b cos x = c with the R Form
42. 40Every Solution of a Trigonometric Equation
43. Radians and Trigonometric Identities (10)