How do you graph and list the amplitude, period, phase shift for #y=sin(1/2)(x-pi)+2#?

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Answer 1 · 2018-06-28T03:05:41

As below.

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

#"Given : y = sin ((x-pi)/2) + 2#

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

#Amplitude = |A| = 1#

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

#"Phase Shift " = -C / B = -(pi/2) / (1/2) = -pi, " " pi " to the LEFT"#

#"Vertical Shift " = D = 2#

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