Polar distance (geometry)

Polar distance (geometry)

In geometry a polar distance, typically denoted "r", is a coordinate in polar coordinate systems ("r", θ) and ("r", θ, "h").

The distance "d" between two points "P"1 and "P"2 with their polar coordinates ("r"1, θ1) and ("r"2, θ2) in two-dimensional circular polar coordinate system is given by the polar distance formula:

: d = sqrt{r_{1}^{2} + r_{2}^{2} - 2 r_{1} r_{2} cos ( heta_{1} - heta_{2})} .

This formula is the well known cosine formula from school level trigonometry. It has been applied to a triangle where two sides have lengths r_{1} and r_{2} and the included angle is heta_{1}- heta_{2} .


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