# What is the Cartesian form of ( -2, (-7pi)/8 ) ?

Cartesian coordinates are

$\left(x , y\right) \setminus \equiv \left(1.8477 , 0.765\right)$

#### Explanation:

The cartesian coordinates $\left(x , y\right)$ of the given point $\left(r , \setminus \theta\right) \setminus \equiv \left(- 2 , - \frac{7 \setminus \pi}{8}\right)$ are given as

$x = r \setminus \cos \setminus \theta$

$= - 2 \setminus \cos \left(\frac{- 7 \pi}{8}\right)$

$= 2 \setminus \cos \left(\frac{\pi}{8}\right)$

$= 1.8477$

$y = r \setminus \sin \setminus \theta$

$= - 2 \setminus \sin \left(\frac{- 7 \pi}{8}\right)$

$= 2 \setminus \sin \left(\frac{\pi}{8}\right)$

$= 0.765$

hence the cartesian coordinates are

$\left(x , y\right) \setminus \equiv \left(1.8477 , 0.765\right)$

Jul 27, 2018

Cartesian coordinates are $\left(1.8478 , 0.7654\right)$

#### Explanation:

For a polar form coordinates $\left(r , \theta\right)$

Cartesian form is $\left(r \cos \theta , r \sin \theta\right)$

Hence, for $\left(- 2 , \frac{- 7 \pi}{8}\right)$

Cartesian form is $\left(- 2 \cos \left(\frac{- 7 \pi}{8}\right) , - 2 \sin \left(\frac{- 7 \pi}{8}\right)\right)$

i.e. (-2(-cos(pi/8)),-2(-sin(pi/8))

and as $\sin \left(\frac{\pi}{8}\right) = \frac{1}{2} \sqrt{2 - \sqrt{2}} = 0.3827$

and $\cos \left(\frac{\pi}{8}\right) = \frac{1}{2} \sqrt{2 + \sqrt{2}} = 0.9239$

and Cartesian coordinates are $\left(1.8478 , 0.7654\right)$