Question

What is the Cartesian form of `(-27,(-9pi)/6))`?

Answer 1

Polar: `(r,theta)=(-27,(-9pi)/6)`
`color(white)("XXX")rarr`Cartesian: `(x,y)=(0,-27)`

Explanation:

Note that an angle of `(-9pi)/6` is equivalent to an angle of `(3pi)/6=pi/2`

This tells us that the point is on the Y-axis (i.e. the `x` coordinate value is `0`)

Since the radius is given as `(-27)` the point is `27` units down the Y-axis from the origin (i.e. at `y=-27`)