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

Mar 1, 2017

$\text{amplitude "=1/2,"period "=360^@," phase shift } = - {90}^{\circ}$

#### Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\textcolor{b l a c k}{y = a \cos \left(b x + c\right) + d}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where amplitude "=|a|," period } = \frac{{360}^{\circ}}{b}$

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

$\text{here } a = \frac{1}{2} , b = 1 , c = {90}^{\circ} , d = 0$

$\Rightarrow \text{amplitude "=|1/2|=1/2," period } = \frac{{360}^{\circ}}{1} = {360}^{\circ}$

$\text{phase shift } = - {90}^{\circ} / 1 = - {90}^{\circ}$