# What is the slope of the tangent line of r=sin(theta/4)/sin(theta/2) at theta=(-3pi)/2?

Dec 20, 2017

-0.48

#### Explanation:

Slope of a polar curve r= $f \left(\theta\right)$ is

The given curve is

=$\sin \frac{\frac{\theta}{4}}{2 \sin \left(\frac{\theta}{4}\right) \cos \left(\frac{\theta}{4}\right)} = \sec \left(\frac{\theta}{4}\right)$

$\frac{\mathrm{dr}}{d \theta} = \frac{1}{4} \sec \left(\frac{\theta}{4}\right) \tan \left(\frac{\theta}{4}\right)$

Slope would thus be

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