## Exercises - Graphing Trigonometric Functions

1. Graph the following for $-2\pi \le x \le 2\pi$.

1. $y = 4\cos x$

2. $y = \sin \frac{2}{3} x$

3. $y = 4\cos(2x - \frac{3\pi}{2})$

4. $y = \sin(x - \frac{\pi}{6})$

5. $y= -\frac{1}{2} \sin x$

2. Graph the following.

1. $y = -\frac{8}{5} \cos (\frac{x}{5} + \frac{\pi}{3})$ over $[-5\pi,10\pi]$

2. $y = 4\sin(2x - \frac{\pi}{6})$ over $[-\pi,2\pi]$

3. $y = \frac{5}{2} \cos (2x + \frac{\pi}{4})$ from $-\pi$ to $\pi$

4. $y = \cos(x + \frac{\pi}{4})$ from $-2\pi$ to $2\pi$

3. Graph the following.

1. $y = 1 + \cos x$ for $-2\pi \le x \le 2\pi$

2. $y = 2 - \sin x$ from $-\pi$ to $\frac{3\pi}{2}$

3. $y = 2 + 2\sin(\frac{x}{3} - \frac{\pi}{6})$ from $-\pi$ to $2\pi$

4. $y = 2 - 3\cos 2x$ over $[-2\pi,\pi]$   (omit finding the $x$-intercepts)

4. Graph the following. Label interecepts and other important features (e.g., asymptotes)

1. $y = -\tan x$ over $[-2\pi,2\pi]$

2. $y = -\sec x$ from $-\pi$ to $\pi$

3. $y = \frac{1}{2} \tan 2x$ from $-\frac{5\pi}{4}$ to $\frac{3\pi}{8}$

4. $y = \csc 3x$ for $-\frac{\pi}{2} \le x \le \frac{5\pi}{6}$

5. $y = 2\tan \frac{x}{2}$ from $-3\pi$ to $\frac{5\pi}{2}$

6. $y = -\csc(4x+\pi)$ from $-\frac{\pi}{2}$ to $\frac{\pi}{2}$