y=5tan1/2(x+pi/4)

Question

What is the period?

Answer 1

argument of tan = (x/2 + pi/8)

when x = 0 right now argument of tan = (pi/8)

what will x be when this is bigger by two pi?
(x/2 + pi/8) = (2 pi + pi/8)

or x/2 = 2 pi

x = 4 pi = period
or
how much x has to increase to go a whole way around 2 pi radians

Answer 2

Oh, sorry, tangent repeats every pi, not 2 pi

so period is 2 pi, not 4 pi