Question

how would i graph 3sec(x + (pi/2))

Answer 1

i know the 3 changes the amplitude but i don't know how i would do that for the graph of sec

Answer 2

Sec x = 1/cos x

so sketch y = 3 cos x from -2π to +2π
then move it horizontally π/2 units to the left.
Draw asymptotes at each of the x-intercepts

Above the upper part of the cosine curve, sketch a curve in the shape of a U between the two asymptotes, with its minimum point placed on the maximum of the cosine curve.

Below the lower part of the cosine curve, sketch a curve in the shape of a upside-down U between the two asymptotes, with its maximum point placed on the minimum of the cosine curve.
Since the maximum of the cosine curve is 3 and its minimum is -3, the secant curve does not exist between -3 and +3

In the following site, you can see the secant graph along with its cosine graph in its simplest form
http://www.squarecirclez.com/blog/explore-the-slope-of-the-tan-curve/5317