You can use the websketch below to observe similarities and differences in the way that the same trig function is graphed in Cartesian and polar coordinate systems.
▹︎ Compare the Graphs
On the left you can see a Cartesian coordinate system, in which a vertical number line (a translation of the `y`-axis) moves from left to right along with the motion of `x`, in the process creating the Cartesian graph.
On the right you can see a polar coordinate system, in which a number line (a rotation of the horizontal axis about the origin) rotates counter-clockwise along with the motion of `theta`, in the process creating the polar graph.
In both cases, the translating or rotating number line has a point indicating the current value of the dependent variable (corresponding to the value of `x` or `theta`). The graph is formed by tracing this dependent-variable point as the number line is translated or rotated to indicate the independent variable.
▹︎︎ The Fine Print
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