Math Insight

Applet: Polar coordinates with polar axes

The red point in the inset polar $(r,\theta)$ axes represent the polar coordinates of the blue point on the main Cartesian $(x,y)$ axes. When you drag the red point, you change the polar coordinates $(r,\theta)$, and the blue point moves to the corresponding position $(x,y)$ in Cartesian coordinates. Alternatively, you can move the blue point in the Cartesian plane directly with the mouse and observe how the polar coordinates represented by the red point change. The coordinate $r$ is the length of the line segment from the point $(x,y)$ to the origin and the coordinate $\theta$ is the angle between the line segment and the positive $x$-axis.

Applet file: polar_coordinates_polar_axes.ggb

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