Question

What is the Cartesian form of `(12,(12pi)/3))`?

Answer 1

Cartesian form:`(color(blue)(12,0))`

Explanation:

The Cartesian form`(x,y)` of the polar coordinates `(12,(12pi)/3)`

`color(blue)(x=rcostheta)=12xxcos((12pi)/3)=12xxcos(4pi)=12xx1`
`color(blue)(x=12`

`color(blue)(y=rsintheta)=12xxsin((12pi)/3)=12xxsin(4pi)=12xx0`
`color(blue)(y=0`

Cartesian form of polar coordinates `(12,(12pi)/3)` is `(color(blue)(12,0))`