There are a few rules from converting a polar equation into cartesian and vice-versa.

1. x^2 + y^2 = r^2, this is easily derived because r^2 is essentially the hypotenuse of a triangle, with theta as its angle

2. By that logic, x = rcos(theta), and y = rsin(theta)

3. So, theta = arctan(y/x)

Those are all of the rules, and when converting from polar to cartesian, one always wants an r touching a trig function.

For example, r = sec(theta), so r = 1/cos(theta), so rcos(theta) = 1, x = 1.

Overall, converting isn't that bad.