# How do you make a sin graph with a period of 4pi?

Oct 24, 2015

I would manipulate the numerical coefficient inside the argument of the sine:

#### Explanation:

If you have the normal sine function (period$= 2 \pi$):
$y = \sin \left(x\right)$
the coefficient conected with the period is the $1$ multiplying the argument as in: $y = \sin \left(x\right) = \sin \left(1 \cdot x\right)$;
this coefficient (call it $c$) helps you to "see" the period of your function that can be evaluated as:
$p e r i o d = \frac{2 \pi}{c} = \frac{2 \pi}{1} = 2 \pi$

Now if you want a period of $4 \pi$ you need that $c = \frac{1}{2}$ so that you get:
$p e r i o d = \frac{2 \pi}{c} = \frac{2 \pi}{\frac{1}{2}} = 2 \pi \cdot 2 = 4 \pi \approx 12.6 r a d$

Finally the complete function will be:

$y = \sin \left(c \cdot x\right) = \sin \left(\frac{1}{2} x\right)$

and graphically:
graph{sin(1/2x) [-18.02, 18.03, -9.01, 9.01]}