Question

What is the Cartesian form of `(-4,(11pi)/4))`?

Answer 1

In Cartesian coordinates, `(-4,(11pi)/4)` = `(2sqrt2, -2sqrt2)`

Explanation:

If you consider that `x=rcosTheta` and `y=rsinTheta`, you can plug in those values from that polar coordinate to find `(x,y)`.

On the unit circle, `theta = (11pi)/4` is equal to `(3pi)/4`.

When you plug it in, `x=-4cos((3pi)/4)` and `y=-4sin((3pi)/4)`.

More simplified, `x=-4*-(sqrt2)/2` and `y=-4*(sqrt2)/2`.

Once everything is finally simplified, you will get `x=2sqrt2` and `y = -2sqrt2`