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Exam 8: Polar Coordinates and Parametric Equations

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Question 51

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

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Question 52

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

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Question 53

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Find the rectangular coordinates for the point whose polar coordinates are given. $( 10,2 \pi / 3 )$

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

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

Plot the point with polar coordinates $( 3,0 )$ and give two other polar coordinate representations, one with $r < 0$ , and the other with $r > 0$ .

Write $7$ in polar form, with $\theta$ between $0$ and $2 \pi$ .

Write $i ( 1 - \sqrt { 3 } i )$ in polar form, with $\theta$ between $0$ and $2 \pi$ .

Sketch the graph of the polar equation. $r = 1 - 2 \sin \theta$

Find the rectangular coordinates for the point whose polar coordinates are given. $( 0,9 \pi )$

Sketch the curve with polar equation $r = 2 - 4 \cos \theta$ .

Find the rectangular coordinates for the point whose polar coordinates are given. $( 8,2 \pi / 3 )$

Sketch the curve represented by , and find a rectangular-coordinate equation for the curve.

Sketch the curve represented by $x = 3 t$ , $y = t - 2$ and find a rectangular-coordinate equation for the curve.

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

Find the rectangular coordinates of the point with polar coordinates $( 1 / \sqrt { 2 } , 3 \pi / 4 )$ .

Write $\sqrt { 5 } ( 1 - i )$ in polar form with argument $\theta$ between $0$ and $2 \pi$ .

Find the polar coordinates of the point with rectangular coordinates $( - 6,6 )$ .

Write the product $z _ { 1 } z _ { 2 }$ , and quotient $z _ { 1 } / z _ { 2 }$ , of $z _ { 1 } = \frac { 2 } { 3 } \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right)$ and $z _ { 2 } = \frac { 1 } { 3 } \left( \cos 250 ^ { \circ } + i \sin 250 ^ { \circ } \right)$ in polar form.

Use a graphing device to sketch the curve represented by $x = 2 \cos 7 t , y = 7 \sin 2 t$ .