Question

How do I convert polar coordinates `(10, -pi/4)` to rectangular coordinates?

Answer 1

The answer is `(sqrt(50), -sqrt(50))`.

This problem is solved using trigonometry. I like to use the mnemonic SYR, CXR, TYX (pronounced sir kicks'er ticks). `sin theta=y/r, cos theta=x/r, tan theta=y/x`.

So rearranging with algebra, we get `x=r cos theta, y=r sin theta`.

Next, substitute the polar coordinates. Make sure that your calculator is in RAD mode. However, `pi/4` is a special angle that you should memorize the ratios.

`x=10 cos (-pi/4), y=10 sin(-pi/4)`

`-pi/4` is in the fourth quadrant, this corresponds with `(sqrt(50), -sqrt(50))`.