# How do you find the amplitude, period and phase shift for y=2sin(theta+45^circ)+1?

Jan 6, 2017

$2 , \pi , - {45}^{\circ}$

#### Explanation:

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

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

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

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

$\text{here " a=2,b=1,c=45^@" and } d = + 1$

$\Rightarrow \text{amplitude " =|2|=2," period } = \frac{2 \pi}{1} = 2 \pi$

$\text{and phase shift } = - {45}^{\circ} / 1 = - {45}^{\circ}$