# What is the slope of the tangent line of #r=theta-sin((10theta)/3-(pi)/8)# at #theta=(pi)/4#?

Slope of the tangent line of

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To find the slope of the tangent line at a given point on a polar curve, you first need to express the curve in Cartesian coordinates and then differentiate the equation with respect to ( \theta ). The slope of the tangent line is given by ( \frac{dy}{dx} ) in Cartesian coordinates.

For the given polar curve ( r = \theta - \sin\left(\frac{10\theta}{3} - \frac{\pi}{8}\right) ), when evaluated at ( \theta = \frac{\pi}{4} ), the Cartesian coordinates are found to be ( x = \frac{\pi}{4} - \sin\left(\frac{5\pi}{6} - \frac{\pi}{8}\right) ) and ( y = \frac{\pi}{4} - \sin\left(\frac{5\pi}{6} - \frac{\pi}{8}\right) ). Then, differentiate both ( x ) and ( y ) with respect to ( \theta ), and find ( \frac{dy}{dx} ) when ( \theta = \frac{\pi}{4} ).

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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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