Question

For each question, the rectangular coordinates of a point are given. Find the polar coordinates of each point. 4. (4, 0) 5. (3, 4) 6. (2, -2)

Answer 1

(4,0) has a magnitude of 4 and an angle of 0.  Thus, it corresponds to 4<0.

(3,4) has a magnitude of sqrt(3^2+4^2), or 5, and a central angle of 

arctan (4/3).


In the case of (2, -2), you can see right away that the magnitude is 2sqrt(2) (Prove it).  What is the central angle?  (2, -2) is in Quadrant 4, so the central angle will be between 270 and 360 degrees:  arctan 2 / (-2).