Question

What is the Cartesian form of `( 6,-pi/6 )`?

Answer 1

Cartesian form of `(6,-pi/6)` is `(3sqrt3,-3)`

Explanation:

Polar coordinates `(r,theta)` are equivalent to Cartesian Coordinates `(rcostheta,rsintheta)`

Hence polar coordinates `(6,-pi/6)` are equivalent to Cartesian Coordinates `(6xxcos(-pi/6),6xxsin(-pi/6))`

i.e. `(6xxcos(pi/6),6xx-sin(pi/6))`

or `(6xxsqrt3/2,-6xx1/2)`

or `(3sqrt3,-3)`