How do you find the period, amplitude and sketch #y=2-sin((2pix)/3)#?

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Answer 1 · 2018-07-31T13:49:29

As below.

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

Given : #y = 2 - sin ((2pix)/3)#

#A = -1, B = (2pi)/3, C = 0, D = 2#

#Amplitude = |A| = 1#

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

Phase Shift #= -C / B = 0#

Vertical Shift # = D = 2#

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