How do you convert the polar coordinate (-2, 0.5236) into cartesian coordinates?

Nov 11, 2016

Polar coordinates are $\left(- 1.732 , - 1\right)$

Explanation:

Polar coordinates $\left(r , \theta\right)$ can be converted into Cartesian coordinates $\left(x , y\right)$ using relation

$x = r \cos \theta$ and $y = r \sin \theta$

Assuming that in $\theta = 0.5236$ angle is given in radians and although $r$ is positive, let its negative value indicate negative or opposite direction.

$x = \left(- 2\right) \times \cos 0.5236 = - 2 \times 0.866 = - 1.732$

and $y = \left(- 2\right) \times \sin 0.5236 = - 2 \times 0.5 = - 1$

Hence, polar coordinates are $\left(- 1.732 , - 1\right)$