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In this lesson, we will learn how to find the derivatives of functions represented in polar coordinates.

Q1:

Consider the polar equation π = 4 π s i n 2 .

Calculate d d π¦ π₯ for π = 4 π s i n 2 .

Find the slope of the tangent to π = 4 π s i n 2 when π = π 8 . Give your answer accurate to three significant figures.

Q2:

Consider the polar equation π = 2 π s i n . We can calculate the derivative d d π¦ π₯ by dividing the derivative d d π¦ π by the derivative d d π₯ π .

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

Calculate the derivative d d π¦ π .

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

Calculate the derivative d d π₯ π .

The derivative d d π¦ π₯ is equal to d d d d ο οΌ ο οΌ . Calculate d d π¦ π₯ .

Use the derivative function to calculate the slope of the tangent to π = 2 π s i n at π = π 6 .

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