Question

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

Answer 1

Important points to the graph are `x` = (`0`, `(3pi)/2`, `3pi`, `(9pi)/2`, `6pi`, `(15pi)/2`, ....). Note that these are all at `(3pi)/2` intervals and maximum and minimum value is `+-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(x)=sinx`, maximum and minimum value is taken as `1` (at `x` = `pi/2`, `(5pi)/2`, `(9pi)/2` ...) etc, and `-1` (at `x` = `(3pi)/2`, `(7pi)/2`, `(11pi)/2` ...).

Apart from that `0` value is taken at (`0`, `+-pi`, `=-2pi` and so on).

These form the important points.

In `f(x)=2sin(x/3)`, maximum value taken is `2`
at `x` = `(3pi)/2`, `(15pi)/2`, `(27pi)/2` ...) etc. and
minimum value taken is `-2`
at `x` = `(9pi)/2`, `(45pi)/2`, `(81pi)/2` ...) etc. and
`0` value is taken at (`0`, `+-3pi`, `+-6pi` and so on).

Note that these are all at `(3pi)/2` intervals and maximum and minimum value is `+-2`.