I converted my polar coordinates into cartesian to get the x and y. You do this by equating the two coordinate systems. For example, since theta is 0, you know that e_r is equal to j hat.

This is what I did.
Given that the two coordinate systems can line up if you put the y axis in the vertical position and the x axis in the horizontal position, there doesn't seem to be too much difficulty converting between the two in this case.
If one didn't start with the y and x axis like that, I can see trig being used to convert between the coordinate systems.
Of course trig can be used to confirm what we see already too.

For finding the x and y coordinates is the best way to use trig?

I converted my polar coordinates into cartesian to get the x and y. You do this by equating the two coordinate systems. For example, since theta is 0, you know that e_r is equal to j hat.

Technically, you can use trig, and you'll get the same answer. Since cos(0) equals 1.

This is what I did.

Given that the two coordinate systems can line up if you put the y axis in the vertical position and the x axis in the horizontal position, there doesn't seem to be too much difficulty converting between the two in this case.

If one didn't start with the y and x axis like that, I can see trig being used to convert between the coordinate systems.

Of course trig can be used to confirm what we see already too.