How do you sketch the graph of y=sin (x/2) ?

Mar 29, 2017

Use the parent function $y = \sin x$ with period $= 4 \pi$ instead of $2 \pi$

Explanation:

Parent function is $y = \sin x$ with period = $2 \pi$

$\frac{x}{2} = \frac{1}{2} x$ changes the period. Period $= \frac{2 \pi}{\frac{1}{2}} = 4 \pi$

Divide the period into $4$ sections:
$x = 0 , x = \pi , x = 2 \pi , x = 3 \pi , x = 4 \pi$

$\left(0 , 0\right)$ is an $x$-intercept
$\left(\pi , 1\right) \approx \left(3.14 , 1\right)$ is a maximum
$\left(2 \pi , 0\right) \approx \left(9.4 , 0\right)$ is an $x$-intercept
$\left(3 \pi , - 1\right) \approx \left(9.4 , - 1\right)$ is a minimum
$\left(4 \pi , 0\right) \approx \left(12.6 , 0\right)$ is an $x$-intercept

graph{sin (x/2) [-10, 10, -5.21, 5.21]}