How do you find the amplitude, period, vertical and phase shift and graph #y=2/3cos[1/2(theta+pi/6)]-2#?

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Answer 1 · 2018-03-01T11:56:40

Amplitude # = 2/3#

Period # = (2pi) / |b| = 4pi#

Phase shift # = c / b = -pi / 6#

Vertical shift # = d = -2#

Standard form of equation is #y = a cos (bx - c) + d#

Given :#y = graph{ (2/3) cos ((x/2)+ (pi/12)) - 2 [-10, 10, -5, 5]} #

#a = 2/3, b = 1/2, c = -(pi/12), d = -2#

Amplitude #a = 2/3#

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

Phase shift # = c / b = -(pi/12) / (1/2) = -pi / 6#

Vertical shift # = d = -2#