6.5 & 6.7 Notes

Determining the transformations to trigonometric functions

6.5 & 6.7 Notes Find the amplitude, period, phase shift, and vertical shift of the trigonometric function.



y

 6 sin      3     2

6.5 & 6.7 Notes

y



A

trig 

B

  

C

  

D

The amplitude of a trigonometric function is the absolute value of the coefficient of trigonometric function.

amplitude:

A

6.5 & 6.7 Notes

y



A

trig 

B

  

C

   The period of a trigonometric function is found by dividing the parent graph’s period by the coefficient of the angle variable, θ.

D T

 parent graph period

B

6.5 & 6.7 Notes

y



A

trig 

B

  

C

   The phase shift is in the direction indicated by the opposite sign of C in an amount equal to the value of C. It may be necessary to factor to find C.

D



C

6.5 & 6.7 Notes

y



A

trig 

B

  

C

   The vertical shift is in the direction indicated by the sign of D in an amount equal to the value of D.

D



D

6.5 & 6.7 Notes Find the amplitude, period, phase shift, and vertical shift of the trigonometric function.

y

 6 sin       3     2

6.5 & 6.7 Notes Find the amplitude, period, phase shift, and vertical shift of the trigonometric function.

y

     180  20

6.5 & 6.7 Notes Find the amplitude, period, phase shift, and vertical shift of the trigonometric function.

y

 tan    2  4   1

6.5 & 6.7 Notes Find the amplitude, period, phase shift, and vertical shift of the trigonometric function.

y y

 10 sin   3sec        4  3  4         5 2