Posted by Anonymous on .
For what values of theta, on the polar curve r=theta, 0<=theta<=2pi, are there horizontal tangent curves? Vertical?
I got one answer for the horizontal tangent. and it's theta = 0 but what are the other ones?/

calculus 
Steve,
since 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