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In this lesson, we will learn how to find the slope of a polar curve at a point and sketch this curve along with its tangent at that point.

Q1:

Find the slope of the tangent line to the curve π = 1 π at π = π .

Q2:

Find the slope of the tangent line to the polar curve π = 2 π c o s at the point π = π 6 .

Q3:

Find the slope of the tangent line to the curve π = ο½ π 3 ο c o s at π = π 2 .

Q4:

Find the slope of the tangent line to the curve π = π c o s at π = π 6 .

Q5:

Find the slope of the tangent line to the curve π = 2 π s i n at π = π 6 .

Q6:

Find the slope of the tangent line to the curve π = 2 β 3 π s i n at π = 5 π 4 .

Q7:

Find the slope of the tangent line to the polar curve π = 1 + π c o s at the point π = π 4 .

Q8:

Find the slope of the tangent line to the curve π = 1 + π s i n at π = π 4 .

Q9:

Find the slope of the tangent line to π = 2 + 4 π c o s at π = π 6 . Round your answer to 3 decimal places.

Q10:

Find the slope of a tangent line to π = 6 + 3 π c o s at ( 3 , π ) .

Q11:

Find the slope of a tangent line to π = 4 π c o s at ( 2 , π 3 ) .

Q12:

Find the slope of a tangent line to π = 1 β π s i n at οΌ 1 2 , π 6 ο .

Q13:

Find the slope of the tangent line to π = 4 + π s i n at the point οΌ 3 , 3 π 2 ο .

Q14:

Find the slope of the tangent line to π = π l n at π = π . Give your answer to 3 decimal places.

Q15:

For the cardioid π = 1 + π s i n , find the slope of the tangent line at π = π 3 .

Q16:

Find the points at which π = 4 π c o s has a horizontal or vertical tangent line.

Q17:

Given a polar curve defined by π = π ( π ) , form an expression for the slope of the curve d d π¦ π₯ in terms of π and π .

Q18:

Find the slope of the tangent line to π = π at π = π 2 .

Q19:

Find the slope of the tangent line to π = 8 π s i n at the point οΌ 4 , 5 π 6 ο .

Q20:

Find the slopes of the tangent lines to π = 2 ( 3 π ) s i n at the tips of the leaves.

Q21:

Find the slopes of the tangent lines to π = 4 ( 2 π ) c o s at the tips of the leaves.

Q22:

Find the slope of the tangent line to the curve π = 1 π at π = 2 π .

Q23:

Find the slope of the tangent line to the polar curve π = 1 + π c o s at the point π = 3 π 4 .

Q24:

Find the slope of the tangent line to the curve π = 1 + π s i n at π = π 3 .

Q25:

Find the slope of the tangent line to the curve π = 2 π s i n at π = π 4 .

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