# How do you write an equation of the cosine function with amplitude 2, period pi, and phase shift pi/2?

Sep 12, 2016

$2 \cos \left(2 x - \pi\right)$

#### Explanation:

The standard form of the $\textcolor{b l u e}{\text{cosine function}}$ is

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{y = a \cos \left(b x + c\right) + d} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

where amplitude = | a | , period $= \frac{2 \pi}{b}$

phase shift $= - \frac{c}{b} \text{ and vertical shift} = d$

here amplitude = 2 and d = 0

period $= \frac{2 \pi}{b} \Rightarrow b = \frac{2 \pi}{\pi} = 2$

phase shift $= - \frac{c}{b} \Rightarrow c = - 2 \times \frac{\pi}{2} = - \pi$

Thus equation is $y = 2 \cos \left(2 x - \pi\right)$