y = sin 2x y = cos 4πx y = cos

www.iTutoring.com  -­‐  NOTES  

 

 

 

 

   

The  Period  of  Sine  and  Cosine  Functions    

   

Name    _________________________________   Date  ___________________      Period  _______  

   

Given the following functions... y = sin bx

y = cos bx

...the period =

2π b

Example:

y = sin 2x

y = cos 4πx

y = cos

x 2

 

         

Graph y = sin 2x

0

       

 

     

Graph y = sin

1 x 2

0

 

             

Graph y = cos 4πx

0

     

 

© iTutoring.com The  Period  of  Sine  and  Cosine  Functions     Pg.  2  

   

Graph y = cos

x 4

0

 

                 

Graph y = 3 sin 4x

0

   

  © iTutoring.com The  Period  of  Sine  and  Cosine  Functions     Pg.  3  

     

Graph y = -9 cos 2x

0

 

                 

Determine the equation for the following graph.

3

-

π 4

-

3π 16

-

π 8

-

0

π 16

π 16

π 8

3π 16

π 4

-3

 

  © iTutoring.com The  Period  of  Sine  and  Cosine  Functions     Pg.  4  

   

Determine the equation for the following graph.

2

-

-π 4

-

3π 4

-

π 2

-

0

π 4

π 4

π 2

3π 4

π 4

-2

 

               

Determine the equation for the following graph.

5

-

-6π 4

-

9π 2

-3π 2

-

0

3π 2

3π 2

3π 2

9π 2

6π 4

-5

     

 

© iTutoring.com The  Period  of  Sine  and  Cosine  Functions     Pg.  5  

     

Determine the equation for the following graph.

4

-

-4π 4

-

-3π 2

-2π 2

-

0

-π 2

π 2

2π 2

3π 2

4π 4

-4

             

 

© iTutoring.com The  Period  of  Sine  and  Cosine  Functions     Pg.  6