# What is the equation of the tangent line of #r=-5cos(-theta-(pi)/4) + 2sin(theta-(pi)/12)# at #theta=(-5pi)/12#?

The polar equation is invalid when

We have a polar equation:

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Then...

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To find the equation of the tangent line at a given point on a polar curve, we first need to express the polar curve in Cartesian coordinates, then find its derivative with respect to theta, and finally evaluate the derivative at the given theta value to determine the slope of the tangent line.

The equation of the polar curve r = -5cos(-θ - π/4) + 2sin(θ - π/12) can be expressed in Cartesian coordinates using the relationships x = r*cos(θ) and y = r*sin(θ). Substituting these expressions into the given equation, we obtain the Cartesian equation of the curve.

After finding the Cartesian equation, we differentiate it with respect to θ to find the derivative, dy/dx. Then, we evaluate dy/dx at θ = -5π/12 to find the slope of the tangent line.

Once we have the slope of the tangent line, we use the point-slope form of the equation of a line, y - y1 = m(x - x1), where (x1, y1) is the point of tangency and m is the slope of the tangent line. Substituting the given point (x1, y1) and the slope m into this equation gives us the equation of the tangent line.

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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 equation of the tangent line of #r=cos(-3theta-(2pi)/3) # at #theta=(-5pi)/3#?
- What is the Cartesian form of #(-64,(5pi)/12)#?
- What is the Cartesian form of #( -8, (-7pi)/3 ) #?

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