Answered: As illustrated in the accompanying…

Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter8: Complex Numbers And Polarcoordinates

Section: Chapter Questions

Problem 8CLT

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As illustrated in the accompanying figure, suppose that a rod with one end fixed at the pole of a polar coordinate system rotates counterclockwise at the constant rate of 1 rad/s. At time t = 0 a bugon the rodis 10 mm from the pole and is moving outward along the rod at the constant speed of 2 mm/s.
(a) Find an equation of the form r = f(θ)forthe path of motion of the bug,assuming that θ = 0when t = 0.
(b) Find the distance the bug travels along the path in part (a) during the first 5 s.Round your answer to the nearest tenth of a millimeter.

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

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