?For the following exercises, find the slope of a tangent line to a polar curve
Chapter 1, Problem 236(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.
\(r=1-\sin \theta ; \quad\left(\frac{1}{2}, \frac{\pi}{6}\right)\)
Text Transcription:
r=f(theta)
x=r cos theta=f(theta) cos theta
y=r sin theta=f(theta) sin theta
r=1-sin theta ; (1/2, pi/6)
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