Question

How do you convert the polar coordinate point `(-2,pi)` into rectangular form?

Answer 1

Polar coordinates `(-2,pi)` in rectangular coordinates are `(2,0)`

Explanation:

Normally `r` in polar coordinates `(r,theta)` are positive, but many times `-r` is allowed and is taken in opposite direction to that indicated by`theta` i.e. `theta+pi`.

Further, polar coordinates `(r,theta)` in rectangular coordinates are `(rcostheta,rsintheta)`

Hence polar coordinates `(-2,pi)` in rectangular coordinates are

`(-2cospi,-2sinpi)` or `(-2xx(-1),-2xx0)` i.e. `(2,0)`