Question

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

Answer 1

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)`