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

Oct 21, 2014

First, the graph of $y = \cos \left(x - \frac{\pi}{2}\right)$ will have some characteristics of the regular cosine function.
I also use a general form for trig functions: $y = a \cos \left(b \left(x - c\right)\right) + d$ where |a| = amplitude, $2 \frac{\pi}{|} b |$ = 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 = $2 \pi$ since the regular period of cosine is $2 \pi$, and there is no multiplier other than a "1" attached to the x.

3) Solving $x - \frac{\pi}{2} = 0$ tells us that there is a phase shift (horizontal translation) of $\frac{\pi}{2}$ 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?