# How do you convert  (1, (3pi )/ 4)  into cartesian form?

Oct 25, 2016

$\text{Polar: "(r,theta)=(1,(3pi)/4)color(white)("XX")rarrcolor(white)("XX")color(green)("Cartesian: } \left(x , y\right) = \left(- \frac{1}{\sqrt{2}} , \frac{1}{\sqrt{2}}\right)$

#### Explanation:

An angle of $\frac{3 \pi}{4}$ is equivalent to a reference angle of $\frac{\pi}{4}$ in the second Quadrant.

Here is a fairly standard image of this relationship

However the polar coordinates tell us that the radius (hypotenuse) needs to be $1$,
so all sides need to be scaled down by dividing by $\sqrt{2}$
giving x-coordinate: $- \frac{1}{\sqrt{2}}$ and y-coordinate: $\frac{1}{\sqrt{2}}$