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The Humongous Book of Trigonometry Problems by W. Michael Kelley

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Converting Between Polar and Rectangular Form

Given points or equations

17.30 In the diagram below, point P has rectangular coordinates (x,y) and polar coordinates (r,θ). Apply trigonometric ratios to express x and y in terms of r and θ.

Note that the diagram contains a right triangle, so you can apply trigonometric ratios to describe the relationship between r, θ, x, and y.

Cross-multiply to solve the equations for x and y, respectively.

You ...

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