Question

What is the Cartesian form of `( 7 , (-35pi)/12 )`?

Answer 1

`(x, y) = (-7 cos (pi/12), -7 sin (pi/12)) = ( -6.7615, -1.8117 )` nearly.

Explanation:

`x = r cos theta and y = r sin theta`.
Here, r = 7 and `theta=-35pi/12`.

Note that `cos (-x) = cos x, sin (-x)=-sinx, cos(3pi-x)=-cos x and sin(3pi-x)=sin x`.
The angle `3pi-x` is in the second quadrant.

`cos (-35pi/12)=cos (pi/12-3pi)=cos(3pi-pi/12)=-cos(pi/12)`.
`sin (-35pi/12)=sin (pi/12-3pi)=-sin(3pi-pi/12)=-sin(pi/12)`