A curve in polar coordinates is given by: r = 7+2 cos 0.Point P is at 0 = 1614a.) Find polar coordinate r for P, with r > 0 and π < 0 < 3³.pb.) Find cartesian coordinates for point P.X =c.) How may times does the curve pass through the origin when 0 < 0 < 2π?Answer:

We have, r = 7 + 2 cos θ Point P is at θ = 16π/14

Answered: A curve in polar coordinates is given…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Find the smallest interval for θ starting with θ min = 0 so that your graphing utility graphs the given polar equation r = 4 sin 2θ exactly once without retracing any portion of it.
Find the points at which the following polar curve has a horizontal or a vertical tangent line. r=2 sin 20 At what points does the polar curve have a horizontal tangent line? OA. (0.2). (0.). (2,0,), and (±2,7 +0₁), where tan 0₁ = √/2 4√/2 4√2 + 3-0₁, where tan 0₁ = √2 OB. (0,0), (0,r), 3x 4√2 O C. 1 (0.). (0.²). (+41² 0₁). and (+4+²,2-0,), where tand, = -√2 4√2) (* 3 3-0₂ √√2 4√3 OD. (0,0), (0,r), , and and t 4√3 -0₁ , where tan 0₁ = √3 At what points does the polar curve have a vertical tangent line? ○ D. (0,0), (0,2), ( + 4√2,0₂), and (± 1 O A. (0,0), (0,), (±2,0₂), and (±2,x+0₂), where tan 8₂ = √√2 4√2 4√2 1 OB. t --0₂ 3 (0.5) - (0.-27). (+44² 0₂2). and (+44² 4-83). Where tan 02 and (2 - 4√³ x-₂): O C. (0.7), (0.37). (+ 4√³,0₂), 3 , where tan 0₂ = 4√/2 3-02, where tan 0₂ = √2 1 √√3
14. (a) Given the point (2, 150°) in polar coordinates, find a corresponding point in rectangular coordinates. (State exact values, not decimal approximations.) Answer: (b) Given the point (-8,– 8) in rectangular coordinates, find a corresponding point in polar coordinates. Express the angle exactly in radians. (Your angle should include Tt). Answer:
What is the polar equation of the vertical line x = 13? Choose the correct answer below. A. r= 13 cos 0 O B. rsin0 = 13 O C. r= 13 sin 0 O D. rcos 0 = 13

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A curve in polar coordinates is given by: r = 7+2 cos 0. Point P is at 0 = 16 14 a.) Find polar coordinate r for P, with r > 0 and π < 0 < ³/4 . b.) Find cartesian coordinates for point P. x = c.) How may times does the curve pass through the origin when 0 < 0 < 2π? Answer: