Explanation Results used: The slope of the tangent at any point is given by d y d x evaluated at that point. If the curve is r = f ( θ ) then d y d x = f ′ ( θ ) sin θ + f ( θ ) cos θ f ′ ( θ ) cos θ − f ( θ ) sin θ . Calculation: The given equation of the curve is r = 1 1 + sin θ . Find the value of d y d x as follows. d y d x = f ′ ( θ ) sin θ + f ( θ ) cos θ f ′ ( θ ) cos θ − f ( θ ) sin θ = − cos θ ( 1 + sin θ ) 2 ⋅ sin θ + 1 1 + sin θ ⋅ cos θ − cos θ ( 1 + sin θ ) 2 ⋅ cos θ − 1 1 + sin θ ⋅ sin θ = − cos θ sin θ + ( 1 + sin θ ) cos θ − cos 2 θ − ( 1 + sin θ ) sin θ = 1 − sin θ − cos 2 θ − sin 2 θ − sin θ Simplify further as follows. d y d x = 1 − sin θ − cos 2 θ − sin 2 θ − sin θ = 1 − sin θ − 1 − sin θ [ ∵ − cos 2 θ − sin 2 θ = − 1 ] = − 1 − sin θ 1 + sin θ Calculate the value of d y d x at point ( 2 3 , − π 6 ) as follows

Calculus, Single Variable: Early Transcendentals (3rd Edition)

3rd Edition

ISBN: 9780134766850

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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Chapter 12.4, Problem 72E

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To find: The equation of the tangent line to the curve r=11+sinθ at the point (23,−π6).

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Chapter 12.4, Problem 71E

Chapter 12.4, Problem 73E

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Chapter 12 Solutions

Calculus, Single Variable: Early Transcendentals (3rd Edition)

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The equation of the tangent line to the curve r = 1 1 + sin θ at the point ( 2 3 , − π 6 ) .

Solution Summary: The author calculates the equation of the tangent line to the curve r=11,+mathrmsintheta .

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To find: The equation of the tangent line to the curve r=11+sinθ at the point (23,−π6).

Want to see the full answer?

Chapter 12 Solutions