How do you find the amplitude, period and phase shift for #y=cos(1/2(theta-90^circ))+2#?

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Answer 1 · 2018-07-12T12:35:57

As below.

Standard form of the cosine function is
#y = A cos (Bx - C) + D#

Given #y = cos (theta/2 - (90/2)^@) + 2#

#y = cos (theta/2 - pi/4) + 2#

#A = 1, B = 1/2, C = pi/4, D = 2#

Amplitude #= |A| = 1#

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

Phase Shift #= -(C/B) = -(pi/4) / (1/2) = -pi/2#, #pi/2# to the LEFT

Vertical Shift #= D = 2#.