Find the slope of the tangent line to the graph of the polar equation at the point specified by the value of 𝜃.

Question

r = 1/𝜃
𝜃 = 𝜋

Answer 1

dy/dx = (dr/d𝜃) / (dx/d𝜃) = (r' sin𝜃 + r cos𝜃) / (r' cos𝜃 - r sin𝜃)
= (-sin𝜃/𝜃^2 + cos𝜃/𝜃) / (-cos𝜃/𝜃^2 - sin𝜃/𝜃)
= (-sin𝜃 + r cos𝜃)/(-cos𝜃 - r sin𝜃) if 𝜃≠0
at 𝜃=𝜋, that means
dy/dx = -𝜋

Answer 2

oops. did you catch my typo?