Polar Coordinates and Equations in Polar Form: Problems with Solutions

Problem 1
Convert $(0,\frac{\pi}{2})$ from polar to Cartesian coordinates.
Problem 2
Convert $(-\sqrt{2},\frac{\pi}{4})$ from polar to Cartesian coordinates.
Problem 3
Convert the equation $y=10$ to polar form.
Problem 4
Convert the equation $x^{2}-y^{2}=4$ to polar form.
Problem 5
Convert the equation $y^{2}=4x$ to polar form.
Problem 6
How do we represent the orange ray in polar coordinates?


Problem 7
Calculate the equation in polar coordinates of this semicircle.


Problem 8
What is the equation in polar coordinates of the blue region?


Problem 9
Convert the polar equation $r\sin\theta =4$ to rectangular equation.
Problem 10
Convert the polar equation $r\sin\theta =r\cos\theta +4$ to rectangular equation.

Problem 11
The points of intersection of the graphs of the functions $r=\sin \theta $ and $r=\sin 2\theta $ are:
Problem 12
The following equations represent $r=\frac{2}{1-2\sin \theta },r=\frac{3}{4+\cos \theta }$
Problem 13
Identify the conic section represented by the equation
$r=\frac{4}{3-2\sin\theta}$
Problem 14
Identify the conic section represented by the equation
$r=\frac{1}{1-\cos\theta }$
Problem 15
Identify the conic section represented by the equation
$r=\frac{2}{1+2\cos\theta }$
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