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 "RealWorld" Page Everything for Calculus
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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. $f(t) = 4.2\sin(π/2−2πt) + 3 = 4.2\sin[π(1/2 − 2t)] + 3$

13. $g(x) = 4 − 1.3\sin[π/2−2.3(x−4)]$

15. $f(x) = \cos(2πx)$

17. $f(x) = 1.5\cos(4π(x−0.375))$

19. $f(x) = 40\cos(π(x−10)/10) + 40$

21. $\sin^2x + \cos^2x = 1$ gives, upon division by $\cos^2x,  \tan^2x + 1 = 1/ \cos^2x = \sec^2x.$

23. $(√3)/2$

31. $4s(t) = 7.5\cos(πt/6) + 87.5$

33. $y_{1}$ is shown in black, $y_{3}$ in red, and $y_{5}$ in yellow.

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 "RealWorld" Page Everything for Calculus
Return to Exercises

We would welcome comments and suggestions for improving this resource. Mail us at:
Stefan Waner (matszw@hofstra.edu) Steven R. Costenoble (matsrc@hofstra.edu)
Last Updated: September, 1996
Copyright © 1996 StefanWaner and Steven R. Costenoble