How do you find the amplitude, period, vertical and phase shift and graph #y=sin(theta-pi/4)#?

1 Answer
Jacob T.
May 28, 2017

Amplitude: #1#
Period: #2pi#
Phase shift: #pi/4# to the right.

Explanation:

First, write the function in a more general form,
#y=A*sin(omega*(x+phi))#
where #abs(A)# is the amplitude, #(2pi)/omega# is the period, and #phi# is the phase shift. Some of these values are omitted as they equal to one.

Now you get amplitude #=abs(A)=1#, Period #=(2pi)/1=2pi#, and #phi=-pi/4#
A negative phase value indicates a shift to the right. So the function shifts to the right by #pi/4#.

http://www.purplemath.com/modules/grphtrig.htm
graph{y=sin(x-pi/4) [-10, 10, -5, 5]}

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