Assignments

In this series of assignments you get familiarized with trigonometric functions such as $\sin(x)$ , $\cos(x)$ and $\tan(x)$ . The angles are measured either in degrees or radians.
There are also a few assignments about the unit circle and some relations between the various trigonometric functions.
Finally we know that some trigonometric functions can be used to demonstrate some trigonometric relations.

1. The following angles are given in degrees. Calculate them in radians.
30, 45, 90, 60, 180, 210, 225, 540

2. In which quadrant do the following angles (in radians) lie:

$\displaystyle\frac{\pi}{6}$ $\displaystyle\frac{5\pi}{6}$ $\displaystyle\frac{5\pi}{3}$ $\displaystyle\frac{13\pi}{3}$

3. Calculate using the table with special angles:

$\sin(\displaystyle\frac{\pi}{3})$ $\cos(\displaystyle\frac{\pi}{6})$ $\tan(\displaystyle\frac{\pi}{4})$

4. Show using the unit circle:

$\sin(-x)=-\sin(x)$

$\cos(-x)=\cos(x)$

$\tan(-x)=-\tan(x)$

5. Show using the unit circle:

$\cos(\displaystyle\frac{\pi}{2}+x)=-\sin(x)$

6. Show using the unit circle:

$\sin(x+\pi)=-\sin(x)$

7. Give the period of:

$\sin(x)$ $\sin(2x)$ $\sin(\displaystyle\frac{1}{3}x)$ $\cos(x)$ $\cos(4x)$ $\tan(\displaystyle\frac{1}{2}x)$

8. Show:

$\sin(3x)=3\sin(x)-4\sin^3(x)$

9. Show:

$1+\tan^2(x)=\displaystyle\frac{1}{\cos^2(x)}$

10. Show for which values of $x$ in the interval $[0,2\pi]$ the function:

$y=\sin(3x)$

takes the value $1$ .

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