# How do you find the rectangular coordinate of (-1, 135 degrees)?

Nov 13, 2015

Polar coordinates $\left(- 1 , {135}^{\circ}\right) \iff$ Rectangular coordinates $\left(\frac{\sqrt{2}}{2} , - \frac{\sqrt{2}}{2}\right)$

#### Explanation:

${135}^{\circ}$ has a reference angle of ${45}^{\circ}$ in Quadrant II

The negative sign on the radius reflects the angle into Quadrant IV

An angle of $\left(- {45}^{\circ}\right)$, that is a ${45}^{\circ}$ reference angle in Quadrant IV
with a hypotenuse (the radius) of $1$
has $\left(x , y\right)$ components $\left(\frac{\sqrt{2}}{2} , - \frac{\sqrt{2}}{2}\right)$