Explanation Given information: Rate of rotation of the pointer = 20 revolutions per minute Distance of the beam form the wall = 8 meters The angle between the line and the beam = θ Formula used: For a right triangle, tan θ = p b . Where, p is the perpendicular. b is the base. θ is the respective angle. Calculation: Consider the distance between the point of light and the point of intersection of the line and the wall be y . The time be t in minutes. So, the rate of movement of the dot is. d y d t . The figure is shown below: From the figure find y . To find y , use the formula tan θ = p b . Substitute 8 for b and y for p in the formula tan θ = p b . tan θ = y 8 y = 8 tan θ Differentiate the above expression with respect to t . d y d t = d d t 8 tan θ = 8 d d t tan θ = 8 sec 2 θ ( d θ d t ) Since, the rate of rotation is 20 revolutions per minute

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

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Question

Chapter 3.9, Problem 22E

To determine

Therate of movement of the dot for θ=π6.

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Chapter 3.9, Problem 21E

Chapter 3.9, Problem 23E

Chapter 3 Solutions

Calculus - Standalone book

Ch. 3.1 - Prob. 1PQ Ch. 3.1 - Prob. 2PQ Ch. 3.1 - Prob. 3PQ Ch. 3.1 - Prob. 4PQ Ch. 3.1 - Prob. 5PQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E

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Therate of movement of the dot for θ = π 6 .

Solution Summary: The author calculates the rate of movement of the dot using the formula mathrmtantheta =pb.

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Therate of movement of the dot for θ=π6.

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Chapter 3 Solutions