## Answers to ExercisesforSection 2: The Six Trigonometric Functions

 1. Modeling with the Sine Function 2. The Six Trigonometric Functions 3. Derivatives of Trigonometric Functions Trigonometric Functions Main Page "Real World" Page

In the following graphs, the first-named function appears in red; the second-named function in yellow.

1.

3.

5.

7.

9.

11. f(t) = 4.2sin(/22t) + 3 = 4.2sin[(1/2 2t)] + 3

13. g(x) = 4 1.3sin[/22.3(x4)]

15. f(x) = cos(2x)

17. f(x) = 1.5cos(4(x0.375))

19. f(x) = 40cos((x10)/10) + 40

21. sin2x + cos2x = 1 gives, upon division by cos2x, tan2x + 1 = 1/ cos2x = sec2x.

23. (3)/2

31. s(t) = 7.5cos(t/6) + 87.5

33. y1 is shown in black, y3 in red, and y5 in yellow.

 y11 = 2 cos x + 23 cos 3x + 25 cos 5x + 27 cos 7x + 29 cos 9x + 211 cos 11x

Here is its graph.

35. The period is approximately 12.6 units

 1. Modeling with the Sine Function 2. The Six Trigonometric Functions 3. Derivatives of Trigonometric Functions Trigonometric Functions Main Page "Real World" Page