Solved: ?For the following exercises, find the slope of a tangent line to a polar curve
Chapter 1, Problem 244(choose chapter or problem)
For the following exercises, find the slope of a tangent line to a polar curve \(r=f(\theta)\). Let \(x=r \cos \theta=f(\theta) \cos \theta\) and \(y=r \sin \theta=f(\theta) \sin \theta\), so the polar equation \(r=f(\theta)\) is now written in parametric form.
Find the points on the interval \(-\pi \leq \theta \leq \pi\) at which the cardioid \(r=1-\cos \theta\) has a vertical or horizontal tangent line.
Text Transcription:
r=f(theta)
x=r cos theta=f(theta) cos theta
y=r sin theta=f(theta) sin theta
-pi leq theta leq pi
r=1-cos theta
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