7.1: Graphs of the Sine, Cosine & Tangent Functions

© 2008 Roy L. Gover(www.mrgover.com)

Learning Goals:

•Graph Trig functions

•Analyze and interpret Trig graphs

Example

Using a table of values, graph

siny tfor2 2t

23 2

202

3 22

Try This

Using a table of values, graph

cosy tfor2 2t

23 2

202

3 22

2

Solution

20

t

Example

Using your graphing calculator, graph ( ) cosg t ton the interval 3 ,2

Try This

On a sheet of paper, compare and contrast the graphs:siny t

cosy t

Example

cosy t

1

-1

0

Animate

Example

sin t

Without using your graphing calculator, find all values of t for which is 1.

Try This

cos t

Without using your graphing calculator, find all values of tfor which

is 1.0 2t k

k=integer

ExampleWithout using your calculator, find all values of t between 0 and 2 for which

sin t

= 12

20

12

Try ThisWithout using your calculator, find all values of t between 0 and 2 for which

cos t= 1

2

5,

3 3t

Analysis

( ) cosf t tFor :

•What is the domain and range?

•What is the unit of measure for the t and axes?

( )f t

DefinitionThe Domain of a function is all possible values of the independent variable (t,x,θ)The Range of a function is all possible values of the dependent variable

, ( ), ( )y f t f

Analysis

( ) cosf t t( ) sinf t t

Compare and contrast the two graphs.

+1

-1

Try This

What is wrong with these statements:

3cos

2t

sin 2t

Try This

Graph the function :

( ) tanf x x

using your graphing calculator

Solution

( ) tanf x x

What is the domain and range?

What are Asymptotes and where do they occur?

Important IdeaAsymptotes occur at all points in the domain where the function is not defined.

(0,-1)

(-1,0) (1,0)

(0,1)

Important IdeaAsymptotes occur at all points in the domain where the function is not defined.

(0,-1)

(-1,0) (1,0)

(0,1)

Try This

Compare and contrast the graphs:

siny t

siny t

1

-1

Try This

Compare and contrast the graphs:

siny t

sin 1.5y t

2.5

1

ExampleFor what values of t on the interval 2 ,2 is:

( )f t• increasing• decreasing

( )f t

• ( ) 0f t 2 2

( ) cosf t t

Example

0 cos 1t

For what values of t on the interval 3 ,2 is:

3 2

( ) cosf t t

Example

3cos

2t

For what values of t on the interval 2 ,2 is:

2 2

( ) cosf t t

3

2

Example

3cos

2t

Name all, exact values of t for which

( ) cosf t t

3

2

Try This

1sin

2t

Name all, exact values of t for which

1

2

( ) sinf t t

26

t n

52

6t n

or

Lesson Close

Define:

•Domain

•Range