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

Apr 7, 2016

$\left(x , y\right) = \left(- 7 \cos \left(\frac{\pi}{12}\right) , - 7 \sin \left(\frac{\pi}{12}\right)\right) = \left(- 6.7615 , - 1.8117\right)$ nearly.

#### Explanation:

$x = r \cos \theta \mathmr{and} y = r \sin \theta$.
Here, r = 7 and $\theta = - 35 \frac{\pi}{12}$.

Note that $\cos \left(- x\right) = \cos x , \sin \left(- x\right) = - \sin x , \cos \left(3 \pi - x\right) = - \cos x \mathmr{and} \sin \left(3 \pi - x\right) = \sin x$.
The angle $3 \pi - x$ is in the second quadrant.

$\cos \left(- 35 \frac{\pi}{12}\right) = \cos \left(\frac{\pi}{12} - 3 \pi\right) = \cos \left(3 \pi - \frac{\pi}{12}\right) = - \cos \left(\frac{\pi}{12}\right)$.
$\sin \left(- 35 \frac{\pi}{12}\right) = \sin \left(\frac{\pi}{12} - 3 \pi\right) = - \sin \left(3 \pi - \frac{\pi}{12}\right) = - \sin \left(\frac{\pi}{12}\right)$