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

TODAY

4-15: TOGETHER AS A CLASS

4-16 DEFINITIONS OF SINE AND COSINE FOR ALL ANGLES

PARTNER PROBLEMS

Complete 4-17 & 4-18

with your partner

CLASS DISCUSSION: REFERENCE ANGLES

PARTNER PROBLEMS

Complete 4-20 & 4-21

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!!

0 22

22

22

22

1 0 0-1.71 .71 .71 .71sin 0

Graphing the Cosine Function• Complete the table of values

• Now plots your points!!

022

22

22

221 0 1-1

.71 .71 .71 .71cos0

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)

,

1,1

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 ____________.

21

Transformations Review

siny A B x C D

Vertical Stretch/ Shrink

Horizontal Stretch/ Shrink

Left/ Right

Up/Down

Reflect over x-axis

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.

ASSIGNMENT

HW 4.1.24-24 to 4-31

(pg. 187)See yu

tmrrw!

ASSIGNMENT

HW 4.1.34-38 to 4-46

(pg. 192)