Polar Coordinates: Videos & Practice Problems

Find the slope of the line given by $\theta =\frac{3\pi }{4}$ when expressed in Cartesian coordinates.

Find the slopes of the lines tangent to the polar curve $r\left(\theta \right)=4+8\cos \theta$ at the origin.

Convert the circle $x^2+(y-3{)}^2=9$ into polar coordinates.

Convert the Cartesian equation $x=-2$ to polar coordinates.

Convert the Cartesian equation $x=y^2$ into polar coordinates.

Convert the polar equation to Cartesian coordinates and describe the curve: $r=2\sec \theta$

Convert the polar equation $r=-2\cos \theta +6\sin \theta$ to Cartesian coordinates and describe the resulting curve.

Convert the polar equation $r=\cos \theta {\csc }^2\theta$ to Cartesian coordinates and describe the resulting curve.

Find all the non-origin intersection points (in polar coordinates) of the curves $r=3\cos \theta$ and $r=1+2\cos \theta$ for $\theta$ in $[0,2\pi )$.

Determine all intersection points (with $\theta \in [0,2\pi )$) of the polar curves $r=1$ and $r=2\sin \theta$.

Convert the polar equation to Cartesian coordinates and describe the curve: $r\sin \theta =-3$

Which of the following represents the Cartesian point $(-3,-3\sqrt{3})$ in polar coordinates?

Convert the Cartesian coordinates $(-1,\sqrt{3})$ to polar coordinates $(r,\theta )$ given that $r\ge 0$, and .

Convert the polar coordinates $(6,\frac{7\pi }{2})$ to Cartesian coordinates.

Convert the polar coordinates $(3,\frac{7\pi }{6})$ to Cartesian coordinates.

Find the Cartesian coordinates of the polar point $(\frac{1}{2},\frac{\pi }{6})$.

Plot the point with polar coordinates $(-5,-\frac{\pi }{4})$.

A point has polar coordinates $r=4$ and $\theta =\frac{2\pi }{3}$. What are its Cartesian coordinates $(x,y)$?

Find the polar equation of the horizontal line $y=7$.

Is the point with polar coordinates $(0,\frac{3\pi }{4})$ located at the origin?

Plot the point with polar coordinates $(-2,-\frac{\pi }{6})$.

Plot the point with polar coordinates $(-3,\frac{\pi }{2})$.

Graph the polar equation $r=5$ on a Cartesian plane.

Sketch the set of points on a Cartesian plane where the distance $r$ from the origin satisfies $3\le r\le 7$.

Do the polar coordinates $(5,\frac{7\pi }{6})$ and $(-5,\frac{\pi }{6})$ describe the same point in the plane?

An aircraft is observed $80$ miles from a radar located at the origin, at an angle of ${300}^{\circ }$ measured clockwise from north. Determine the polar coordinates $(r,\theta )$, where the angle $\theta$ is measured counterclockwise from the positive $x$-axis, following the standard convention for polar coordinates.

Sketch the graph of $r=2-\cos \theta$ by creating a table of values. Consider values of $\theta$ between $0$ and $2\pi$.

Sketch the graph of $r=3-3\sin \theta$ by creating a table of values. Consider values of $\theta$ between $0$ and $2\pi$.

Sketch the graph of $r^2=9\sin \theta$ by creating a table of values.

Sketch the graph of $r=\cos 3\theta$.