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QUESTION

# What is the graph of y=cos(x-pi/2)?

First, the graph of y=cos(x-pi/2) will have some characteristics of the regular cosine function. I also use a general form for trig functions: y = a cos(b ( x - c)) + d where |a| = amplitude, 2pi/|b| = period, x = c is the horizontal phase shift, and d = vertical shift.

1) amplitude = 1 since there is no multiplier other than "1" in front of the cosine.

2) period = 2pi since the regular period of cosine is 2pi, and there is no multiplier other than a "1" attached to the x.

3) Solving x - pi/2=0 tells us that there is a phase shift (horizontal translation) of pi/2 to the right.

The bright, red graph is your graph! Compare it to the dotted, blue graph of cosine. Do you recognize the changes itemized above?