What is the Cartesian form of ( -7 , (-3pi)/4 ) ?

Dec 2, 2017

The cartesian equivalent is $\left(\frac{7 \sqrt{2}}{2} , \frac{7 \sqrt{2}}{2}\right)$.

Explanation:

In polar we have:
$x = r \cdot \cos \left(\setminus \theta\right)$
$y = r \cdot \sin \left(\setminus \theta\right)$

In the given ordered pair $r = - 7$ and $\theta = - \frac{3 \pi}{4}$.

Substituting gives:
$x = - 7 \cos \left(- \frac{3 \pi}{4}\right) = - 7 \left(- \frac{\sqrt{2}}{2}\right) = \frac{7 \sqrt{2}}{2}$
$y = - 7 \sin \left(- \frac{3 \pi}{4}\right) = - 7 \left(- \frac{\sqrt{2}}{2}\right) = \frac{7 \sqrt{2}}{2}$

So the cartesian equivalent is $\left(\frac{7 \sqrt{2}}{2} , \frac{7 \sqrt{2}}{2}\right)$.