# Lesson 12

Tangent

### Problem 1

Here is a graph of $$f$$ given by $$f(\theta) = \tan(\theta)$$.

1. Are $$\frac{\pi}{2}$$ and $$\frac{3\pi}{2}$$ in the domain of $$f$$? Explain how you know.
2. What are the $$\theta$$-intercepts of the graph of $$f$$? Explain how you know.

### Problem 2

The function $$f$$ is given by $$f(\theta) = \tan(\theta)$$. Which of the statements are true? Select all that apply.

A:

$$f$$ is a periodic function

B:

The domain of $$f$$ is all real numbers.

C:

The range of $$f$$ is all real numbers.

D:

The period of $$f$$ is $$2\pi$$.

E:

The period of $$f$$ is $$\pi$$.

### Problem 3

Here is the unit circle.

If $$\tan(a) > 1$$ where could angle $$a$$ be on the unit circle?

### Problem 4

Here is a point on the unit circle.

1. Explain why the line going through $$(0,0)$$ and $$P$$ has slope $$\frac{1}{2}$$.
2. What is the tangent of the angle represented by $$P$$? Explain how you know.

### Problem 5

For which angles $$\theta$$ between 0 and $$2\pi$$ is $$\cos(\theta) < 0$$? Explain how you know.

(From Unit 6, Lesson 9.)

### Problem 6

It is 3:00 a.m.

The function $$f$$ is given by $$f(x) = x^2$$.
1. Write an equation for the function $$g$$ whose graph is the graph of $$f$$ translated 3 units left and then reflected over the $$y$$-axis.
2. Write an equation for the function $$h$$ whose graph is the graph of $$f$$ reflected over the $$y$$-axis and then translated 3 units to the left.
3. Do $$g$$ and $$h$$ have the same graph? Explain your reasoning.