## Answers to ExercisesforSection 2: The Six Trigonometric Functions

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.

$y_{11} =$$\frac{2}{π}$$\cos x +$$\frac{2}{3π}$$\cos 3x +$$\frac{2}{5π}$$\cos 5x +$$\frac{2}{7π}$$\cos 7x +$$\frac{2}{9π}$$\cos 9x +$$\frac{2}{11π}$$\cos 11x$

Here is its graph.

35. The period is approximately $12.6$ units

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