The Trigonometric Functions
by
Stefan Waner and Steven R. Costenoble

Answers to Exercises
for
Section 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

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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

+

2 3

cos 3x

+

2 5

cos 5x

+

2 7

cos 7x

+

2 9

cos 9x

+

2 11

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

Return to Exercises

Stefan Waner (matszw@hofstra.edu)

Steven R. Costenoble (matsrc@hofstra.edu)

Last Updated: September, 1996 Copyright © 1996 StefanWaner and Steven R. Costenoble