# Lesson 4Off on a TangentDevelop Understanding

The equation of a parent function is given. Write a new equation with the given transformations. Then sketch the new function on the same graph as the parent function. (If the function has asymptotes, sketch them in.)

### 1.

• vertical shift: up

• horizontal shift: left

• vertical stretch or shrink:

Equation:

Graph:

### 2.

• vertical shift: up

• horizontal shift: right

• vertical stretch or shrink:

Equation:

### 3.

• vertical shift: none

• horizontal shift: left

• vertical stretch or shrink:

Equation:

### 4.

• vertical shift:

• horizontal shift: left

• vertical stretch or shrink (amplitude):

Equation:

## Set

### 5.

Triangle is a right triangle. .

Use the information in the figure to label the length of the sides and measure of the angles.

### 6.

Triangle is an equilateral triangle. and is an altitude.

Use the information in the figure to label the length of the sides, the length of , and the exact length of .

Label the measure of angles and .

### 7.

Use what you know about the unit circle and the information from the figures in problems 5 and 6 to fill in the table.

function

### 8.

Label all of the points and angles of rotation in the unit circle.

### 9.

Fill in the chart for .

### 10.

Explain how the answers in problem 9 support the statement that is classified as an odd function.

## Go

### 11.

Given triangle with angle being a right angle, what is ?

### 12.

Identify the quadrants in which is positive.

### 13.

Identify the quadrants in which is negative.

### 14.

Identify the quadrants in which is positive.

### 15.

Explain why it is impossible for .

### 16.

Name the angles of rotation (in radians) for when .

### 17.

For which trigonometric function does a positive rotation and a negative rotation always give the same value?

### 18.

Explain why in the unit circle, .

Explain why .