# Lesson Worksheet: Slope of a Polar Curve Mathematics • Higher Education

In this worksheet, we will practice finding the derivatives of polar curves and the slope of a polar curve.

Q1:

Find the slope of the tangent line to the polar curve at the point .

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Q2:

Find the slope of the tangent line to the polar curve at the point .

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Q3:

Consider the polar equation .

Calculate for .

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Find the slope of the tangent to when . Give your answer accurate to two decimal places.

Q4:

Consider the polar equation . We can calculate the derivative by dividing the derivative by the derivative .

To calculate the derivative , we first need to introduce the variable by multiplying both sides of the equation by and then substituting. Write this equation in terms of .

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Calculate the derivative .

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Similarly, to calculate the derivative , we first need to introduce the variable by multiplying both sides of the original equation by and then substituting. Write this equation in terms of .

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Calculate the derivative .

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The derivative is equal to . Calculate .

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Use the derivative function to calculate the slope of the tangent to at .

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Q5:

Find the slope of the tangent line to the curve at .

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Q6:

Find the slope of the tangent line to the curve at .

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Q7:

Find the slope of the tangent line to the curve at .

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Q8:

Find the slope of the tangent line to the curve at .

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Q9:

Find the slope of the tangent line to the curve at .

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Q10:

Find the slope of the tangent line to the curve at .

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