What is the phase shift, vertical displacement with respect to #y=sinx# for the graph #y=3sin(1/2)(x-pi/4)-10#?

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Answer 1 · 2018-06-17T13:41:16

Phase Shift # = -C / B = -pi/4, pi/4# to the left.

Vertical Shift # = D = -10#

#y = 3 sin (1/2) (x - pi/4) - 10#

Standard form of sine function is #y = A sin (Bx - C) + D#

#A = 3, B = (1/2), C = pi/8, D = -10#

Amplitude #= |A| = 3#

Period # = (2pi) / |B| = (2pi) / (1/2) = 4pi#

Phase Shift # = -C / B = (-pi/8) / (1/2) = -pi/4, pi/4# to the left.

Vertical Shift # = D = -10#

graph{3 sin(x/2 - pi/8) - 10 [-10, 10, -5, 5]}