# What is the equation of the tangent line of #r=cos(-3theta-(2pi)/3) # at #theta=(-5pi)/3#?

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To find the equation of the tangent line of ( r = \cos(-3\theta - \frac{2\pi}{3}) ) at ( \theta = -\frac{5\pi}{3} ), we first need to find the polar coordinates ((r, \theta)) at the given point. Then, we can use the polar coordinate form of the equation of a tangent line, which is ( r = x\cos(\theta) + y\sin(\theta) ), where ( (x, y) ) is a point on the tangent line.

By substituting ( \theta = -\frac{5\pi}{3} ) into ( r = \cos(-3\theta - \frac{2\pi}{3}) ), we find the value of ( r ) at the given point. Then, we can convert the polar coordinates to Cartesian coordinates to get ( (x, y) ). Finally, we substitute these values into the equation of the tangent line to obtain the equation.

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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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