Quiz 11.4:


Question:

Find the slope of \( r = \cos \theta \) at \( \theta = \frac{\pi}{6} \)


Solution:

\( m = \frac{dy}{dx} = \frac{(-\sin \theta)(\sin \theta)+(\cos \theta)(\cos \theta )}{(-\sin \theta)(\cos \theta)-(\cos \theta)(\sin \theta } = \frac{(-1/2)(1/2)+(\sqrt{3}/2)(\sqrt{3}/2)}{(-1/2)(\sqrt{3}/2)-(\sqrt{3}/2)(1/2)} =\frac{-1}{\sqrt{3}} \)
JCCC
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