# What is the amplitude and period of y=2sinx?

Feb 15, 2018

$2 , 2 \pi$

#### Explanation:

$\text{the standard form of the "color(blue)"sine function}$ is.

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

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

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

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

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

Feb 15, 2018

amplitude: $2$
period: ${360}^{\circ}$

#### Explanation:

the amplitude of $y = \sin x$ is $1$.

$\left(\sin x\right)$ is multiplied by $2$, i.e. after the function $\sin x$ has been applied, the result is multiplied by $2$.

the result of $\sin x$ for the graph $y = \sin x$ is $y$ at any point on the graph.

the result of $2 \sin x$ for the graph $y = \sin x$ would be $2 y$ at any point on the graph.

since $y$ is the vertical axis, changing the coefficient of $\left(\sin x\right)$ changes the vertical height of the graph.

the amplitude is the value of the distance between the $x$-axis and the highest or lowest point on the graph.

for $y = \left(1\right) \sin x$, the amplitude is $1$.

for $y = 2 \sin x$, the amplitude is $2$.

the period of a graph is how often the graph repeats itself.

the graph of $y = \sin x$ will repeat its pattern every ${360}^{\circ}$. $\sin {0}^{\circ} = \sin {360}^{\circ} = 1$, $\sin {270}^{\circ} = \sin {630}^{\circ} = - 1$, etc.

(the graph shown is $y = \sin x$ where ${0}^{\circ} \le x \le {720}^{\circ}$)

if the value that the function $\sin$ is being applied to changes, the graph will change along the $x$-axis.

e.g. if the value is changed to $y = \sin 2 x$, $y$ will be $\sin {90}^{\circ}$ at $x = {45}^{\circ}$, and $\sin {360}^{\circ}$ at $x = {180}^{\circ}$.

the range of the values that $y$ can take will stay the same, but they will be at different points of $x$.

if the coefficient of $x$ is increased, the highest and lowest points on the graph will seem closer together.

however, the function in question does not the coefficient of $\left(x\right)$ - only the coefficient of $\left(\sin x\right)$.

the range of values that $y$ can take is doubled, but $x$ will repeat itself at the same points.

the amplitude is $2$, and the period is ${360}^{\circ}$.