Question

How do you convert `(3, -3)` to polar form?

Answer 1

`(r, theta)=(3sqrt 2, (7pi)/4)` or `(3sqrt 2, -pi/4)`

Explanation:

Use `(x, y) = (3, -3)= (r cos theta, r sin theta)`

`r=sqrt(x^2+y^2)=sqrt(9+9)=3 sqrt 2`

`cos theta = 1/sqrt 2>0 and sin theta -1/sqrt2<0`

So, theta is in the 4th quadrant and is `(7pi)/4` and this direction is

same as for `-pi/4`.

Now, `(r, theta)=(3sqrt 2, (7pi)/4))` or `(3sqrt 2, -pi/4)`.