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December 20, 2014

December 20, 2014

Posted by **Anonymous** on Wednesday, November 2, 2011 at 11:56am.

I got one answer for the horizontal tangent. and it's theta = 0 but what are the other ones?/

- calculus -
**Steve**, Wednesday, November 2, 2011 at 1:07pmsince r = θ

x = r cosθ

y = r sinθ

dy/dθ = r' sinθ + r cosθ = sinθ + θcosθ

dx/dθ = r' cosθ - r sinθ = cosθ - θsinθ

dy/dx = (sinθ + θcosθ)/(cosθ - θsinθ)

You are correct that dy/dx = 0 when θ=0

It is also zero when x = 2.04 and 4.88

(approximately)

The tangent is vertical when the denominator is zero: x = 0.84 and 3.45

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