# How do you write the equation of the sine function with an amplitude of 4, a period of pi/2 and a phase shift of - pi/4?

Jun 12, 2016

$y = 4 \sin \left(4 x + \pi\right)$

#### Explanation:

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

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

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

c is the phase shift and d , the vertical shift

here a = 4 , b$= \frac{2 \pi}{\frac{\pi}{2}} = 4$

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

Substitute these values into standard form

$\Rightarrow y = 4 \sin \left(4 x + \pi\right) \text{ is the equation}$