Question

find the slope of the curve r=cos 2theta at theta =pi/6

Answer 1

Hi, I can help if you're still around.

Answer 2

As we're on this, do you know what a derivative is?

Answer 3

Differentiating the given function with respect to theta, we have
\[\huge r=\cos 2\theta \rightarrow \frac{dr}{d \theta} = \frac{d}{d \theta} \cos 2 \theta\]
\[\huge \rightarrow \frac{dr}{d \theta} = -2 \sin 2 \theta\]
at \[\theta = \frac{\pi}{6} = 30^0 we have...\]
\[\huge \rightarrow \frac{dr}{d \theta} = -2 \sin (2 \times 30^0) = - 2 \sin 60^0 = -\sqrt3\]
Hence sloppe of the curve is \[\huge - \sqrt 3\]
@stellawong38