# What is the slope of the tangent line of #r=theta-cos(-4theta+(2pi)/3)# at #theta=(7pi)/4#?

The reference Tangents with Polar Coordinates gives us this formula for

Substitute

Substitute

The slope, m, is equation [3] evaluated at

Here is a graph of r

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To find the slope of the tangent line of ( r = \theta - \cos(-4\theta + \frac{2\pi}{3}) ) at ( \theta = \frac{7\pi}{4} ), you first need to find the derivative of ( r ) with respect to ( \theta ) (denoted as ( \frac{dr}{d\theta} )). Then, evaluate ( \frac{dr}{d\theta} ) at ( \theta = \frac{7\pi}{4} ) to get the slope of the tangent line at that point.

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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.

- What is the area enclosed by #r=theta # for #theta in [0,pi]#?
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- What is the Cartesian form of #(100,(-17pi)/16))#?
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- What is the equation of the line that is normal to the polar curve #f(theta)=-5theta- sin((3theta)/2-pi/3)+tan((theta)/2-pi/3) # at #theta = pi#?

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