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distance formula between two polar coordinates. Recall the distance formula in polar coordinates is d² equals r1² plus r2² minus 2r1r2 times cosine of theta 2 minus theta 1. We can also use the polar coordinates distance formula to help us come up with the polar equation for a circle centered at the origin.
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Thus the distance between two points P x1 y1 and Q x2 y2 is. And plugging these points into the distance formula from the polar coordinate system we getDsqrt1222-212cos2pi-piDsqrt5-4cospiDsqrt5-4-1Dsqrt54. 2 r1 r2 times the cosine of the angle between them which is theta 2 minus theta 1.
So the distance formula looks like this.
This is an application of the cosine law. Just like the Distance Formula for and coordinates there is a way to find the distance between two polar coordinates. So we can make this r1theta 1 and r2theta 2. Similarly any polar coordinate is identical to the coordinate with the negative radial component and the opposite direction adding 180 to the polar angle.
