sketch the graph of y = 3sec (x - Π/2) for -2Π ≤ x ≤ 2Π

Hint:

y = 3sec (x - Π/2) = 3csc (x)

You graph y = 3sin (x) first, and then graph y = 3csc (x).

Attn: y = 3sin (x) and y = 3csc (x) share the same vertices. There are four vertical asymptotes: x = -2pi, x = -pi, x = 0, x = pi, and x = 2pi.

The shape is similar as follow:

∪ .∪

..∩ .∩