SOLUTION: Sinusoidal Functions Without graphing, determine the amplitude, period, equation of the axis, phase shift, domain, and range of the function y=20 cos(9x-81°)-2''.

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Question 1140761: Sinusoidal Functions
Without graphing, determine the amplitude, period, equation of the axis, phase shift, domain, and range of the function y=20 cos(9x-81°)-2''.

Found 2 solutions by t0hierry, greenestamps:
Answer by t0hierry(194) (Show Source):
You can put this solution on YOUR website!
The Amplitude is 20.
When 9x = 81 + 2 pi
then x = 9 + 2pi/9
and the cosine repeats itself, so
the period = 2 pi/9
The phase shift is 81
Domain is infinity
Range is y = [-22 , 18]

Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

One part of the response from the other tutor needs to be corrected.

To find the phase shift, you need to factor out the coefficient of x.

-->

The phase shift is 9 degrees, not 81 degrees.

His explanation of how to determine the period is 2pi/9 (or 360/9 degrees) is a good one. Here is another way to see that is the period.

The cosine function takes on all its values in a range of 2pi radians. So this function takes on all its values when 9x ranges from 0 to 2pi:

<-- the period is 2pi/9.