1

What you will learn

How to graph a basic sin and cos function

Objective: 6-3 Graphing Sine and Cosine Functions

2

Review of Functions A quick review of yesterday:

..\..\..\Desktop\Trigonometry_UnitCircle_SixFunctions.gsp

Objective: 6-3 Graphing Sine and Cosine Functions

3

A Little Vocabulary If a “function” has repeating values over

an interval, the function is said to be periodic.

The interval of “repeat” is the period of the function.

Objective: 6-3 Graphing Sine and Cosine Functions

4

“Real World” Example

x-20 -10 10 20

y

-100

-50

50

100 Yearly temperatures in Baltimore and Asheville

Objective: 6-3 Graphing Sine and Cosine Functions

5

Determining If a Function is Periodic Page 360.

Objective: 6-3 Graphing Sine and Cosine Functions

6

Graphing a Basic Sine Function

x

yBasic Values

Objective: 6-3 Graphing Sine and Cosine Functions

7

The Basic Sin Graph

x-10 -5 5 10

y

-2

-1

1

2

2

n4. The x-intercepts are located at

5. y-intercept is 0

6. Maximum values are y=1 and occur when

7. Minimum values are y = -1 and occur when

nx 2

2

Characteristics:1. Period is .2. Domain: all real3. Range: all real between -1 and 1

nx 2

2

3

Objective: 6-3 Graphing Sine and Cosine Functions

8

Determine Values from a Graph

Example: Find by referring to the graph of the sine function2

9sin

Objective: 6-3 Graphing Sine and Cosine Functions

9

You Try Find by referring to the graph of the

sine function. 3sin

Objective: 6-3 Graphing Sine and Cosine Functions

10

Finding Angle Values Given the Graph Find the values for which sin = 0 is

true.

Objective: 6-3 Graphing Sine and Cosine Functions

11

You Try Find the value of for which sin = -1 is

true.

Objective: 6-3 Graphing Sine and Cosine Functions

12

Graphing on an Interval Example: Graph y = sin x for 53 x

Objective: 6-3 Graphing Sine and Cosine Functions

13

You Try Graph y = sin x for 42 x

Objective: 6-3 Graphing Sine and Cosine Functions

14

Graphing a Basic Cosine Function

x

yBasic Values

Objective: 6-3 Graphing Sine and Cosine Functions

15

The Basic Cos Graph

x-10 -5 5 10

y

-2

-1

1

2

2

n

4. The x-intercepts are located at

5. y-intercept is 1

6. Maximum values are y=1 and occur when where n is an even integer

7. Minimum values are y = -1 and occur when where n is an odd integer

nx

2

Characteristics:1. Period is .2. Domain: all real3. Range: all real between -1 and 1

n

Objective: 6-3 Graphing Sine and Cosine Functions

16

Determining What Type of Graph Determine whether the graph represents y =

sin x or y = cos x, or neither.

9 8 7

1

-1

Objective: 6-3 Graphing Sine and Cosine Functions

17

You Try Determine whether the graph represents y =

sin x or y = cos x, or neither.

4

1

-1

5 6

Objective: 6-3 Graphing Sine and Cosine Functions

18

Homework page 363, 13-15 all, 20-30 even, 32-36

even, 37-39 all.