Exam 8: Polar Coordinates and Parametric Equations

Convert the rectangular coordinates to polar coordinates with $r > 0 \text { and } 0 \leq \theta < 2 \pi$ $( - 2 \sqrt { 3 } , - 2 )$

For the point with polar coordinates $P ( - 6,0 )$ find two other polar coordinate representations of P with $r > 0$

Convert the polar equation to rectangular coordinates. $r / 3 = \csc \theta$

Test the polar equation for symmetry with respect to the polar axis, the pole, and the line $\theta = \pi / 2$ . $r = 3 \cos \theta \csc \theta$

Sketch a graph of the polar equation. $r = \sqrt { 3 } + 2 \sin \theta$

Convert the equation to polar form. $x ^ { 2 } - y ^ { 2 } = 9$

Find the rectangular coordinates for the point whose polar coordinates are given. $( \sqrt { 2 } , - 5 \pi / 3 )$

Find $( 2 \sqrt { 3 } - 2 i ) ^ { 12 }$ using DeMoivre's Theorem.

Use a graphing device to sketch the curve represented by $x = 2 \sin t , y = \cos 2 t$ .