How do you determine the amplitude, period, and shifts to graph #y=3sin(1/3x+ pi/2)-2#?

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Answer 1 · 2018-06-07T06:43:07

As below.

#y = 3 sin (x/3 + pi/2) -2#

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

#A = 3, B = 1/3, C = -pi/2, D = -2#

#Amplitude = |A| = 3#

#"Period " = (2pi) / |B| = (2pi) / 3#

#"Phase Shift " = -C / B = - (pi/2) / 3 = -(pi/6)#, #color(crimson)(pi/6 " to the left")#

#"Vertical Shift " = D = -2#

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