Question

How do you sketch the graph of `y= cos (2πx- π/2) +1`?

Answer 1

As below

Explanation:

Standard form `y = A cos (Bx - C) + D`

Given `y = cos (2pix - pi/2) + 1`

`A = 1, B = 2pi, C = pi/2, D = 1`

`Amplitude = |A| = 1`

`"Period " = (2pi) / |B| = (2pi) / (2pi) = 1`

`"Phase Shift " = -C / B = (pi/2) / (2pi) = 1/4`, `color(crimson)(1/4 " to the right"`

`"Vertical Shift " = D = 1`

graph{cos (2pix - pi/2) + 1 [-10, 10, -5, 5]}