Exam 8: Polar Coordinates and Parametric Equations

Test the polar equation for symmetry. $r ^ { 2 } = 36 \sin 2 \theta$

Find $( \sqrt { 2 } - \sqrt { 2 } i ) ^ { 16 }$ using DeMoivre's Theorem.

Find the polar coordinates of the point with rectangular coordinates $( - \sqrt { 2 } , - \sqrt { 2 } / \sqrt { 3 } )$ .

Sketch the curve represented by $x = t \sin t$ , $y = \cos t$ .

Sketch the curve represented by $x = 5 \sin t + 1$ , $y = 4 \cos t + 1$ and find a rectangular-coordinate equation for the curve.

Test the polar equation for symmetry. $r = 4 + 8 \cos \theta$

Sketch the graph of the polar equation. $r = 4 \theta$ , $\theta > 0$

Sketch the curve with polar equation $r = \sin \theta \tan \theta$ .

Plot the point with polar coordinates $( 1 , \pi / 4 )$ and give two other polar coordinate representations, one with $r < 0$ , and the other with $r > 0$ .

Write $- 3 + 4 i$ in polar form, with $\theta$ between $0$ and $2 \pi$ .

Write the product $z _ { 1 } z _ { 2 }$ and quotient $z _ { 1 } / z _ { 2 }$ , if $z _ { 1 } = 8 \left( \cos \frac { 11 \pi } { 6 } + i \sin \frac { 11 \pi } { 6 } \right)$ and $z _ { 2 } = 2 \sqrt { 3 } \left( \cos \frac { n } { 3 } + i \sin \frac { n } { 3 } \right)$ in polar form.

Convert the equation to polar form. $y = 7$

For the point with polar coordinates $P ( 1 , \pi / 3 )$ find two other polar coordinate representations of P with $r < 0 .$

Sketch the curve with polar equation $r = 4 \sin 4 \theta$ .

Convert the polar equation to rectangular coordinates. $r / 6 = \sec \theta$

Find the rectangular coordinates of the point with polar coordinates $( 0 , \pi / 27 )$ .

Sketch the curve represented by $x = 3 \sin t$ , $y = \cos t$ , $0 \leq t \leq 2 \pi$ and find a rectangular-coordinate equation for the curve.

Sketch the curve represented by $x = \cos ^ { 2 } t$ , $y = \cos ^ { 6 } t$ and find a rectangular-coordinate equation for the curve.

Sketch the curve represented by $x = 1 - t$ , and find a rectangular-coordinate equation for the curve.

Convert the equation $x + y = 2$ to polar form.