How do you find the period, amplitude and sketch #y=cos(2pix-pi/2)+1#?

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Answer 1 · 2018-07-13T02:01:28

As below.

#y = cos (2pix - pi/20 + 1#

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

#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#

#"Vertical Shift " = D = 1#

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