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 $= d = -2$

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