For these types of problems you need to recall that:Originally Posted bysimon

Inverting these relations gives:

So for question a)

(2,-6) => x = 2, y = -6

is a reference angle. The point (2,-6) is in the 4th quadrant, so your angle measured from the +x axis is 360 - 71.5651 = 288.435 degrees.

Thus: (2,-6) => (2sqrt(10), 288.435 degrees).

For question b)

(3, 150 degrees) => r = 3, = 150 degrees

Thus: (3, 150 degrees) => (-2.59808, 1.5).

(And note that it is, in fact, in the second quadrant as the original coordinates state.)

-Dan