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]}

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