# How do you find the amplitude and period of y=1/2sintheta?

Apr 15, 2018

Amplitude is $\textcolor{b l u e}{\frac{1}{2}}$

$\text{Period} = \textcolor{b l u e}{2 \pi}$

#### Explanation:

If we express the sine function in the following way:

$y = a \sin \left(b x + c\right) + d$

Then:

$\setminus \setminus \setminus \boldsymbol{|} a | \setminus \setminus \setminus = \text{the amplitude}$

$\boldsymbol{\frac{2 \pi}{|} b |} \setminus \setminus = \text{the period}$

$\boldsymbol{\frac{- c}{b}} = \text{the phase shift}$

$\setminus \setminus \setminus \setminus \boldsymbol{d} \setminus \setminus \setminus = \text{the vertical shift}$

For given function we have:

$| a | = \frac{1}{2}$

So amplitude is $\textcolor{b l u e}{\frac{1}{2}}$

$| b | = 1$

$\text{period} = \frac{2 \pi}{|} b | = \frac{2 \pi}{1} = \textcolor{b l u e}{2 \pi}$

GRAPH: