Question

What is the period and amplitude for `cos(pi/5)(x)`?

Answer 1

As below.

Explanation:

Standard form of cosine function is `y = A cos (Bx - C) + D`

Given `y = cos ((pi/5) x)`

`A = 1, B = pi/5, C = D = 0`

Amplitude `= |A| = 1`

Period `= (2 pi) / |B| = (2pi) / (pi/5) = 10`

Phase Shift `= -C / B = 0`

Vertical Shift `= D = 0`

graph{cos ((pi/5) x) [-10, 10, -5, 5]}