# 4.1.2: What Does the Unit Circle Tell Me? 4.1.2: What Does the Unit Circle Tell Me?

Today you will learn how sine and cosine can be viewed in terms of the unit circle; develop the Fundamental Pythagorean Identity; and use the unit circle, the Fundamental Pythagorean Identity, and right triangles to find the values of trigonometric functions.

Homework 4.1.1

Homework 4.1.1

Homework 4.1.1

## Complete 4-22 & 4-23 with your partner

4.1.3: How Can I Build a Wave?

Today you will generate the graphs of sine and cosine using the unit circle as well as find the domain, range, and intercepts for the sine and cosine graphs.

### Graphing the Sine Function

• Complete the table of values

## sin 0

0  2 2 .71

1 2 0  2 2 2  .71

  .71

-1  2 2   .71

0

### Graphing the Cosine Function

• Complete the table of values

## cos 0

1 2 2  .71

0  2 2   .71

-1  2 2   .71

0 2 2  .71

1

### Domain and Range

• The domain is the section of graph where the function exists from left to right. The domain is also thought of as the set of all possible inputs that make the function true. • The range is the section of the graph where the function exists from bottom to top. The range is also thought of as the set of all possible outputs that make the function true.

### Domain and Range

For the non-transformed sine and cosine function:    , 1,1   • The domain is ______________. (interval notation) • The range is ________________. (interval notation)

### Period and Amplitude

• Graphically, the period is one “cycle” of the graph. That is… the horizontal distance the graph travels before it repeats the same pattern. • Amplitude is the height from the line of oscillation. Or I will call this the ‘center line.’ • NOT from highest point to lowest point!!!

### Period and Amplitude

For the non-transformed sine and cosine functions: 

### Transformations Review

Reflect over x-axis

y

 

A

sin   

D

Vertical Stretch/ Shrink Left/ Right Horizontal Stretch/ Shrink Up/Down

• Tomorrow is the Chapter 3 Individual Test!

• Thursday you will be working on both homework assignments in class (4.1.2 & 4.1.3). Please work together and help each other out.

• Friday we will be transforming the basic sine and cosine graphs. If you have a solid grasp of what the basic sine and cosine graphs look like and what their basic characteristics are (maximum points, minimum points, where it crosses center line (crossings), period, amplitude, domain, range, etc.) the easier it will be to transform the graphs.

HW 4.1.2

4-24 to 4-31 (pg. 187) See yu tmrrw!

HW 4.1.3

4-38 to 4-46 (pg. 192)