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Find the slope of the tangent line to the given polar curve at the point specified by the value of θ.

r=6/θ, θ=π

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  1. y = r sinθ
    x = r cosθ

    dy = sinθ dr + r cosθ dθ
    dx = cosθ dr - r sinθ dθ

    so, the slope of the tangent line is

    dy/dx = (sinθ dr + r cosθ dθ)/(cosθ dr - r sinθ dθ)

    at θ=π, dy/dx = r dθ/dr = r(-6/r^2) = -π^2/6

    so, now we have a point and a slope, so the tangent line is

    y = -π^2/6 (x + 6/π)

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