What is the period, amplitude, and frequency for #f(x)=3+3 cos (\frac{1}{2}(x-frac{\pi}{2}))#?

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Answer 1 · 2018-03-06T08:09:51

Amplitude #= 3#, Period #= 4pi#, Phase shift #= pi / 2#, Vertical shift #= 3#

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

Given #y = 3 cos ((x/2) - (pi /4) ) + 3#

#:. a = 3, b = (1/2), c = -(pi/4) , d = 3#

Amplitude #= a = 3#

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

Phase shift # = -c / b = (pi/4) / (1/2) = pi / 2#, #color(blue)((pi/2)#to the right.

Vertical shift # = d = 3#

graph{3 cos ((x/2) - (pi / 4)) + 3 [-9.455, 10.545, -2.52, 7.48]}