What is the Cartesian form of (-1,(22pi)/4))?

Feb 2, 2017

(0,1)

Explanation:

First of all, angle $\frac{22 \pi}{4}$ is $\frac{11 \pi}{2}$ which is equivalent to 4pi +(3pi)/2 that is $\frac{3 \pi}{2}$ because $4 \pi$ just adds 0 to the angle $\frac{3 \pi}{2}$

So, first we move by an angle of $\frac{3 \pi}{2}$ radians anti-clockwise
around the pole from starting position of 0 radians. This is shown in the figure below, as point P. Now since r= -1, we move in the opposite direction of r=1 for angle of $\frac{3 \pi}{2}$ . This positions has been indicated by point P' in the figure.

As is now evident from the figure, cartesean coordinates for$\left(- 1 , \frac{22 \pi}{4}\right)$ would be point P' (0,1)