Practice Polar Coordinates in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A coordinate system where each point in the plane is described by a distance r from the origin and an angle \theta from the positive x-axis, written as (r, \theta).
Instead of 'go right 3, up 4' (Cartesian), polar says 'go 5 units in the direction of 53°.' It's how a radar works—distance and direction from a central point. Some shapes that look complicated in Cartesian coordinates become beautifully simple in polar.
Example 1
easyConvert the polar coordinates (4, \frac{\pi}{3}) to rectangular (Cartesian) coordinates.
Example 2
mediumConvert the rectangular point (-3, 3) to polar coordinates with r > 0 and 0 \le \theta < 2\pi.
Example 3
mediumConvert the equation x^2 + y^2 = 6x to polar form.
Example 4
hardFind all polar representations of the point with rectangular coordinates (0, -5) where -2\pi \le \theta < 2\pi.