# j-james/math All my math notes, now in Markdown.

View the Project on GitHub j-james/math

# Graphs of Tangent and Reciprocal Functions

## Learning Targets

You should be able to

• Graph tangent functions
• Graph reciprocals

## Concepts / Definitions   ### Examples

#### Example 1

Graph $f(\theta) = 4\sec 2\theta +1$

#### Example 2

Solve $\cot x = -\sqrt 3$ on $(-2\pi, 2\pi)$ (no calculator)

## Exercises

### In Class

#### No Calculator

2. Convert $\frac{4\pi}{3}$ radians to degrees.
4. Name a co-terminal angle to $\frac \pi 4$
5. Evaluate $\sin 1.5\pi$
6. What is the reference angle for $-\frac{9\pi}{4}$?
7. If $\sin(-t) = \frac 79$, then $\sin t = ?$
8. If $\cos\theta = \frac{\sqrt 3}{2}$, then $\cos(\theta-\pi) = ?$
9. If $\sin\theta = -\frac{\sqrt 3}{2}$, find $\theta$ on $[0,2\pi)$
10. If $\tan\theta = 0$, then find $\theta$ on $[0,2\pi)$
11. If $\sec\theta = 2$, then find $\theta$ on $[0,2\pi)$
12. Find the coordinate on the unit circle that corresponds to an angle of $t = -\frac{5\pi}{6}$
13. If $\sin = -\frac{\sqrt 2}{2}$ and $\cos x>0$, then $\cos x = ?$
14. Evaluate $\tan \frac{2\pi}{3}$ and $\sec\frac \pi 3$
15. Graph $f(x) = 2\sin (2x-\pi)-3$

#### Calculator

1. Convert 1.485 radians to D°M’S” form.
2. What is the radius of a circle whose arc length is 20 cm and whose angle is 60°?
3. The radius of a disc is 6 cm. Find the linear speed of a point on the circumference if the disc is rotating at 600 revolutions per min.
4. A bicycle is moving at a rate of 12 mi/hr, and the diameter of its wheels is about 2 feet. Find the angular speed of the wheels in radians per minute. (1mi = 5280 ft)
5. Evaluate $\sec(40\degree 10’)$
6. The point (-8, 15) is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions.
7. You are 50ft from a building. The angle of elevation to the top of the building is 30 degrees. How tall is that building?
8. What is the measure of the smallest angle of a 3-4-5 triangle in radians?
9. A signal buoy bobs up and down with height h of its transmitter that is 5 feet above sea level. The waves vary from 1ft to 9ft, and there are 3.5 seconds between the maximun heights. Write a model that represents the height of the transmitter from sea level, starting at its maximun height, during this period of waves.

### Homework

Graph

1. $f(x) = \csc\frac x2 + 3$
2. $f(x) = 2\tan\pi x -2$
3. $f(\theta) = -\cot 2\theta$
4. $f(y) = 3\sec(3y-\pi)+1$
5. For $f(x) = 0.5\sec(2x-\pi)$,
1. Where are all the asymptotes?
2. What is the domain?
3. What is the range?
6. Is tangent an odd or even function?
7. Find $x$ for $\csc x = 1$ on $[0,2\pi)$ (no calculator)
8. Find $x$ for $\cot x = 1$ on $[0,2\pi)$ (no calculator)