How do you find the amplitude, period, and shift for y=2cos(3x+pi/2)?

Amplitude$= \left\mid 2 \right\mid = 2$
Period $= \frac{2 \pi}{3} = 2.0943951023932$
Shift $= - \frac{\pi}{6} = - 0.5235987755983$

Explanation:

Let the form be $y = a \cos \left(b x - c\right)$

Amplitude $= \left\mid a \right\mid$

Period $= \frac{2 \pi}{\left\mid b \right\mid}$

Shift $= \frac{c}{b}$

Computations:

Arrange the equation first

$y = 2 \cos \left(3 x + \frac{\pi}{2}\right)$

$y = 2 \cdot \cos \left(3 x - - \frac{\pi}{2}\right)$

Amplitude $= \left\mid a \right\mid = \left\mid 2 \right\mid = 2$

Period $= \frac{2 \pi}{\left\mid b \right\mid} = \frac{2 \pi}{\left\mid 3 \right\mid} = \frac{2 \pi}{3} = 2.0943951023932$

Shift $= \frac{c}{b} = \frac{- \frac{\pi}{2}}{3} = - \frac{\pi}{6} = - 0.5235987755983$

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