Question

Help!
a. Find all polar coordinates of Cartesian point (2, 2√3). Use radian angle measure.
b. Find Cartesian coordinates of polar point (-1, 3π/4).

Answer 1

Well you can write (2,2 sqrt(3)) as 4(1/2, sqrt(3)/2) This corresponds to a magnitude (or radius/modulus/etc) of 4 and an angle of 60 degrees as cos(60) = 1/2 and sin(60) = sqrt(3)/2. However:
\[(r,\theta) = (r, \theta + 2 k \pi); k \in \mathbb{Z}\]
Therefore your angle is:
\[\frac{\pi}{3} \pm 2k \pi; k \in \left\{0, 1,2,3,...\right\}\]