# What is the slope of #r=sintheta# at #theta=pi#?

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To find the slope of the polar curve ( r = \sin(\theta) ) at ( \theta = \pi ), we can first find the derivative of ( r ) with respect to ( \theta ), then evaluate it at ( \theta = \pi ).

The derivative of ( r ) with respect to ( \theta ) is given by:

[ \frac{dr}{d\theta} = \frac{d(\sin(\theta))}{d\theta} = \cos(\theta) ]

Evaluating this derivative at ( \theta = \pi ):

[ \frac{dr}{d\theta} \bigg|_{\theta = \pi} = \cos(\pi) = -1 ]

Therefore, the slope of the polar curve ( r = \sin(\theta) ) at ( \theta = \pi ) is ( -1 ).

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