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## Main Question or Discussion Point

Is there a way to find all points of intersection in a polar co ordinate graph without the need to draw the graph. i/e USing algebra??? If so, how?

- Thread starter ehabmozart
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- #1

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Is there a way to find all points of intersection in a polar co ordinate graph without the need to draw the graph. i/e USing algebra??? If so, how?

- #2

mfb

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If you have equations for whatever should be intersecting, look for points where both equations are satisfied.

- #3

Mark44

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For example, consider r = cos(θ) and r = sin(θ). Equating the right sides gives sin(θ) = cos(θ), or tan(θ) = 1, so θ = ##\pi/4 + n\pi##, with n an integer.

The two graphs also intersect at the origin, which you probably wouldn't know if you didn't graph them. The reason this intersection point doesn't appear from the algebra work above is that each graph "sees" the origin in different coordinates. For r = cos(θ), the point at the origin is (0, ##\pi/2##). For r = sin(θ), the points at the origin are (0, 0) and (0, ##\pi##).

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