# 4.1.2: What Does the Unit Circle Tell Me?

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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

Today

4-15: Together as a class

4-16 Definitions of sine and cosine for all angles

Complete 4-17 & 4-18 with your partner
Partner problems Complete 4-17 & 4-18 with your partner

Class Discussion: Reference Angles

Complete 4-20 & 4-21 with your partner
Partner problems Complete 4-20 & 4-21 with your partner

Complete 4-22 & 4-23 with your partner
Partner problems 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.

Today . . .

Graphing the Sine Function
Complete the table of values Now plots your points!! 1 -1

Graphing the Cosine Function
Complete the table of values Now plots your points!! 1 -1 1

Comparing the Sine and the Cosine Graph

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:
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: The period is ____________. The amplitude is ____________.

Transformations Review
Reflect over x-axis Left/ Right Vertical Stretch/ Shrink Up/Down Horizontal Stretch/ Shrink

Looking Ahead 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!
assignment HW to 4-31 (pg. 187) See yu tmrrw!

Assignment HW to 4-46 (pg. 192)

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