Question

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Answer 1

cos is periodic with period 2pi. That means cos(x) = cos(x + s*2pi) for any integer s. So, to find the period of cos(pi/2 * t) you need to find the period x for which cos(pi/2 * (t + x)) = cos(pi/2 * t + 2pi). So, you need to solve pi/2 * (t+x) = pi/2 * t + 2pi. Equivalently, pi/2 * t + pi/2 * x = pi/2 * t + 2pi. Then pi/2 * x = 2pi. x = 4. So, this says that cos(pi/2(t + 4)) = cos(pi/2 * t). So, the period is 4.

Answer 2

thanks @scarydoor :)