# What are the important points to graph f(x)=2 sin (x/3)?

Feb 13, 2016

Important points to the graph are $x$ = ($0$, $\frac{3 \pi}{2}$, $3 \pi$, $\frac{9 \pi}{2}$, $6 \pi$, $\frac{15 \pi}{2}$, ....). Note that these are all at $\frac{3 \pi}{2}$ intervals and maximum and minimum value is $\pm 2$.

#### Explanation:

When we draw sine graphs, we do not try to plot all the points but initially only important points.

In the graph $f \left(x\right) = \sin x$, maximum and minimum value is taken as $1$ (at $x$ = $\frac{\pi}{2}$, $\frac{5 \pi}{2}$, $\frac{9 \pi}{2}$ ...) etc, and $- 1$ (at $x$ = $\frac{3 \pi}{2}$, $\frac{7 \pi}{2}$, $\frac{11 \pi}{2}$ ...).

Apart from that $0$ value is taken at ($0$, $\pm \pi$, $= - 2 \pi$ and so on).

These form the important points.

In $f \left(x\right) = 2 \sin \left(\frac{x}{3}\right)$, maximum value taken is $2$
at $x$ = $\frac{3 \pi}{2}$, $\frac{15 \pi}{2}$, $\frac{27 \pi}{2}$ ...) etc. and
minimum value taken is $- 2$
at $x$ = $\frac{9 \pi}{2}$, $\frac{45 \pi}{2}$, $\frac{81 \pi}{2}$ ...) etc. and
$0$ value is taken at ($0$, $\pm 3 \pi$, $\pm 6 \pi$ and so on).

Note that these are all at $\frac{3 \pi}{2}$ intervals and maximum and minimum value is $\pm 2$.