Question

What is the Cartesian form of `( 2 , (13pi)/3 )`?

Answer 1

`"Polar:" (r,theta)=(2,(13pi)/3)color(white)("X")harr"Cartesian:" (x,y)=(1,sqrt(3))`

Explanation:

`theta= (13pi)/3 = 2xx(2pi)+pi/3`

Since `2pi` represents a complete circle
`(13pi)/3` is equivalent (in terms of location) to `pi/3`

Here is the standard `pi/3` triangle (with `r=2`)

from which we can see `x=1` and `y=sqrt(3)`