Consider the following diagram:

(a) Suppose What is the value of ?

(b) Give a possible value for the angle between 0 and . Note that there are infinitely many possibilities for outside this interval.

(c) Suppose we were to consider one of the other three points in the diagram. Would the value of change? What about the value of ? Use symmetry to find the polar coordinates of the other three points. Each angle should be given in radians between 0 and .
Point Q has polar coordinates

(, )

Point R has polar coordinates
(, )

Point S has polar coordinates
(, )

(d) Use your work above to convert the Cartesian coordinates to polar coordinates. [Hint: take note of what quadrant the point is in.]

(, )

(e) In general, if is an arbitrary point in the first quadrant, how can you find an equivalent polar coordinate ?

What if is in the second quadrant?