Explanation Given: The angle between the curve C 1 and curve C 2 at P is θ and the tangent lines toC 1 and C 2 at P have slopes m 1 and m 2 respectively. Calculations: Let α 1 and α 2 be the angles formed by the tangent lines to the curvesC 1 and curve C 2 with respect to the x -axis. Then, m 1 = tan α 1 m 2 = tan α 2 Also, the angle between the lines is: θ = | α 2 − α 1 | Using the identity tan ( x − y ) = tan x − tan y 1 + t

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 3.6, Problem 57PS

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To show: tanθ=|m2−m1|1+m1m2

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Chapter 3.6, Problem 56PS

Chapter 3.6, Problem 58PS

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Chapter 3 Solutions

Calculus

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tan θ = | m 2 − m 1 | 1 + m 1 m 2

Solution Summary: The author calculates the angle between the curves C 1 and C 2 at P using the identity mathrmtan(x-y).

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Chapter 3 Solutions