# What is the slope of the polar curve #f(theta) = sectheta - csctheta # at #theta = (3pi)/8#?

The slope of the tangent line of a function at a point is equal to the derivative of the function at that point.

With that being said, let's take the derivative

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The slope of the polar curve ( f(\theta) = \sec(\theta) - \csc(\theta) ) at ( \theta = \frac{3\pi}{8} ) can be found by differentiating the equation with respect to ( \theta ) and then evaluating the derivative at ( \theta = \frac{3\pi}{8} ). The derivative of ( \sec(\theta) ) is ( \sec(\theta) \tan(\theta) ), and the derivative of ( \csc(\theta) ) is ( -\csc(\theta) \cot(\theta) ). Therefore, the derivative of ( f(\theta) ) is ( \sec(\theta) \tan(\theta) + \csc(\theta) \cot(\theta) ). Evaluating this at ( \theta = \frac{3\pi}{8} ), we get the slope of the curve.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- What is the Cartesian form of #(18,(-51pi)/8))#?
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- What is the Cartesian form of #( -9 , ( - 15pi)/2 ) #?
- What is the Cartesian form of #(33,(-pi)/8)#?

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