# Convert (4, 5π/6) to rectangular form?

May 23, 2018

rectangular form:

$\left(x , y\right) = \left(- 2 \sqrt{3} , 2\right)$

#### Explanation:

show:

$x = r \cdot \cos \theta$

$y = r \cdot \sin \theta$

$x = 4 \cdot \cos \left(5 \frac{\pi}{6}\right) = 4 \cdot \left(- \frac{\sqrt{3}}{2}\right) = - 2 \sqrt{3}$

$y = 4 \cdot \sin \left(5 \frac{\pi}{6}\right) = 4 \cdot \frac{1}{2} = 2$

rectangular form:

$\left(x , y\right) = \left(- 2 , 2\right)$

Note that:

$5 \frac{\pi}{6} = 150$ lies in the second quadrant

since $\cos \theta$ is negative in the second quadrant

$\cos \left(5 \frac{\pi}{6}\right) = - \cos \left(\frac{\pi}{6}\right) = - \frac{\sqrt{3}}{2}$

since $\sin \theta$ is positive in the second quadrant

$\sin \left(5 \frac{\pi}{6}\right) = \sin \left(\frac{\pi}{6}\right) = \frac{1}{2}$