Question

How do you graph `r=2sintheta`?

Answer 1

Please see below.

Explanation:

As `r=2sintheta`, at `theta=0,pi/4,pi/2,(3pi)/4` and `pi`

`r` takes the values `0,sqrt2,2,sqrt2,0`

Thus these represents points `(0,0)`, `(sqrt2,pi/4)`, `(2,pi/2)`, `(sqrt2,(3pu)/4)` and `(0,pi)`.

We can select more such points, say by having `theta=pi/6,pi/3,(2pi)/3, (5pi)/6` and corresponding value of `r` would be `r=1,sqrt3,sqrt3,1` and points are `(1,pi/6)`, `(sqrt3,pi/3)`, `(sqrt3,(2pi)/3)` and `(1,(5pi)/6)`.

The gaph will appear as follows:

It is a circle with center at `(1,pi/2)` and radius `1`

and as `r=2sintheta` means `r^2=2rsintheta`

in rectangular coordinates, it is equivalent to `x^2+y^2=2y`