What is the Cartesian form of (-2,(88pi) /16)?

1 Answer
Sep 8, 2016

Polar (r,theta)=(-2,(88pi)/16) is equivalent to Cartesian (x,y)=(0,2)

Explanation:

theta=(88pi)/16=5pi +pi/2
Since 2pi makes one full circle
(88pi)/16 is equivalent to (3pi)/2

As an angle (3pi)/2 maps on to the negative Y-axis in the Cartesian system.

The polar point (-2,(88pi)/16) is therefore a distance of (-2) from the origin measured down the negative Y-axis;
but (-2) down the negative Y-axis is the same as +2 up the positive Y-axis.

Therefore (-2,(88pi)/16) is a point on the Y-axis at y=2;
that is at (x,y)=(0,2)