graph the functions, what is the period of each function?

Question

cos(x - π⁄2)

Answer 1

The graph has the same shape as the cosine graph but is shifted to the right by ¶/2. The period is 2∏. Divide the period by 4 to get ∏/2. The five key x values are ∏/2, ∏/2 +∏/2 or ∏, ∏+∏/2 or 3∏/2, 3∏/2 +∏/2 = 2∏, 2∏+∏/2 = 5∏/2

The 5 key points are (∏/2 , 1), (∏,0), (3∏/2,-1), (2∏,0), (5∏/2,1) and this is one period

Answer 2

period = 2pi

the pi/2 is a phase shift which doesn't change the period of the standard cosine function