# How do you find the amplitude, period, and shift for y = -5sin(x/2)?

Dec 21, 2017

Amplitude $= | A | = | - 5 | = 5$

Period $\text{ } = \frac{2 \Pi}{\frac{1}{2}} = 4 \Pi$

Shift $\text{ } = \frac{C}{B} = \frac{0}{\frac{1}{2}} = 0$

The Vertical Shift (D) = 0

#### Explanation:

Investigate the graph given below:

The General Form of the equation of the Cos function:

$\textcolor{g r e e n}{y = A \cdot S \in \left(B x + C\right) + D}$, where

A represents the Vertical Stretch Factor and its absolute value is the Amplitude.

B is used to find the Period (P):$\text{ } P = \frac{2 \Pi}{B}$

C, if given, indicates that we have a place shift BUT it is NOT equal to $C$

The Place Shift is actually equal to $x$ under certain special circumstances or conditions.

D represents Vertical Shift.

We observe that

Amplitude $= | A | = | - 5 | = 5$

Period $\text{ } = \frac{2 \Pi}{\frac{1}{2}} = 4 \Pi$

Shift $\text{ } = \frac{C}{B} = \frac{0}{\frac{1}{2}} = 0$

The Vertical Shift (D) = 0

Hope this helps.

Dec 21, 2017

$5 , 4 \pi , 0 , 0$

#### Explanation:

$\text{the standard form of the sine function is }$

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

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

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

$\text{here } a = - 5 , b = \frac{1}{2} , c = d = 0$

$\text{amplitude "=|-5|=5," period } = \frac{2 \pi}{\frac{1}{2}} = 4 \pi$

$\text{there is no phase / vertical shift}$