Question

What is the polar form of `( -4,27 )`?

Answer 1

`(27.29,1.72)`

Explanation:

The polar form is `(r,theta)`
To find r use the formula `r^2=x^2+y^2`

`r=sqrt((-4)^2+27^2)~~27.29`

To find `theta` use the formula `tan theta =y/x` but make sure you look at the quadrant that the point is in to determine the right `theta` using the rules for the quadrants

`tan theta = 27/-4`

`theta=tan^-1(27/-4)~~-1.423717971` but the point is in quadrant two so we add `pi`. Note that `theta` is usually in radian.

Hence, `theta ~~ 1.72`