How do you graph #y=sin(1/2)(x+pi)#?

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Answer 1 · 2018-08-14T13:40:50

As below.

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

Given #y = sin ((1/2)(x + pi))#

#A = 1, B = (1/2), C = -pi, D = 0#

#Amplitude = |A| = 1#

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

Phase Shift # = (-C) / B = (-(-pi/2)) / (1/2) = pi#, #color(red)(pi)# to the RIGHT

Vertical Shift #= D = 0#

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