Explanation The given polar curves are, r = cot θ and r = 2 cos θ . The points of intersection of the curves r = cot θ and r = 2 cos θ is obtained by equating both the curves. cot θ = 2 cos θ cos θ sin θ = 2 cos θ cos θ = 2 sin θ cos θ cos θ − 2 sin θ cos θ = 0 cos θ ( 1 − 2 sin θ ) = 0 So, either cos θ = 0 or 1 − 2 sin θ = 0 . If cos θ = 0 , then θ = π 2 , 3 π 2 . Similarly, if 1 − 2 sin θ = 0 , the value of θ is given by, 1 − 2 sin θ = 0 2 sin θ = 1 θ = sin − 1 ( 1 2 ) θ = π 6 , 5 π 6 Substitute θ = π 2 in equation r = cot θ and r = 2 cos θ . r = cot ( π 2 ) = 0 r = 2 cos ( π 2 ) = 0 Substitute θ = 3 π 2 in equation r = cot θ and r = 2 cos θ

Essential Calculus: Early Transcendentals; MAC 2311 Sequence| MAC 2281Sequence USF (Essential Calculus)

2nd Edition

ISBN: 9781285101552

Author: James Stewart

Publisher: Cenage

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Chapter 9, Problem 34RE

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Chapter 9, Problem 33RE

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Essential Calculus: Early Transcendentals; MAC 2311 Sequence| MAC 2281Sequence USF (Essential Calculus)

Ch. 9.1 - 14 Sketch the curve by using the parametric...Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - (a) Eliminate the parameter to find a Cartesian...Ch. 9.1 - (a) Eliminate the parameter to find a Cartesian...

Ch. 9.1 - (a) Eliminate the parameter to find a Cartesian...Ch. 9.1 - (a) Eliminate the parameter to find a Cartesian...Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - 15-18 Describe the motion of a particle with...Ch. 9.1 - 15-18 Describe the motion of a particle with...Ch. 9.1 - Describe the motion of a particle with position...Ch. 9.1 - Describe the motion of a particle with position...Ch. 9.1 - Prob. 19E Ch. 9.1 - Prob. 20E Ch. 9.1 - Prob. 21E Ch. 9.1 - Match the parametric equations with the graphs...Ch. 9.1 - Graph the curve x = y 2 sin y.Ch. 9.1 - Graph the curves y = x3 4x and x = y3 4y and...Ch. 9.1 - (a) Show that the parametric equations x = x1 +...Ch. 9.1 - Use a graphing device and the result of Exercise...Ch. 9.1 - Find parametric equations for the path of a...Ch. 9.1 - (a) Find parametric equations for the ellipse...Ch. 9.1 - Use a graphing calculator or computer to reproduce...Ch. 9.1 - Use a graphing calculator or computer to reproduce...Ch. 9.1 - Compare the curves represented by the parametric...Ch. 9.1 - Prob. 32E Ch. 9.1 - Derive Equations 1 for the case /2 Ch. 9.1 - Let P be a point at a distance d from the center...Ch. 9.1 - If a and b are fixed numbers, find parametric...Ch. 9.1 - A curve, called a witch of Maria Agnesi, consists...Ch. 9.1 - Prob. 37E Ch. 9.1 - Prob. 38E Ch. 9.1 - Investigate the family of curves defined by the...Ch. 9.1 - The swallowtail catastrophe curves are defined by...Ch. 9.1 - Graph several members of the family of curves with...Ch. 9.1 - Graph several members of the family of curves x =...Ch. 9.1 - The curves with x = a sin nt, y = b cos t, called...Ch. 9.1 - Prob. 44E Ch. 9.2 - Find dy/dx. x = t sin t, y = t2 + t Ch. 9.2 - Find dy/dx. x = 1/t, y=tet Ch. 9.2 - Find an equation of the tangent to the curve at...Ch. 9.2 - Find an equation of the tangent to the curve at...Ch. 9.2 - Find an equation of the tangent to the curve at...Ch. 9.2 - Find an equation of the tangent to the curve at...Ch. 9.2 - Find an equation of the tangent to the curve at...Ch. 9.2 - Find equations of the tangents to the curve x =...Ch. 9.2 - Find dy/dx and d2y/dx2. 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For which values t of...Ch. 9.2 - Prob. 13E Ch. 9.2 - Prob. 14E Ch. 9.2 - Find the points on the curve where the tangent is...Ch. 9.2 - Find the points on the curve where the tangent is...Ch. 9.2 - Prob. 17E Ch. 9.2 - Prob. 18E Ch. 9.2 - Prob. 19E Ch. 9.2 - Prob. 20E Ch. 9.2 - Show that the curve x = cos t, y = sin t cos t has...Ch. 9.2 - Graph the curve x = cos t + 2 cos 2t, y = sin t +...Ch. 9.2 - Prob. 23E Ch. 9.2 - Prob. 24E Ch. 9.2 - At what points on the curve x = 2t3, y = 1 + 4t ...Ch. 9.2 - Prob. 26E Ch. 9.2 - Prob. 27E Ch. 9.2 - Find the area enclosed by the curve x = t2 2t,...Ch. 9.2 - Find the area enclosed by the x-axis and the curve...Ch. 9.2 - Prob. 30E Ch. 9.2 - Prob. 31E Ch. 9.2 - Prob. 32E Ch. 9.2 - Prob. 33E Ch. 9.2 - Prob. 34E Ch. 9.2 - Prob. 35E Ch. 9.2 - Prob. 36E Ch. 9.2 - Prob. 37E Ch. 9.2 - Prob. 38E Ch. 9.2 - Prob. 39E Ch. 9.2 - Prob. 40E Ch. 9.2 - Prob. 41E Ch. 9.2 - Prob. 42E Ch. 9.2 - Prob. 43E Ch. 9.2 - Find the length of the loop of the curve x = 3t ...Ch. 9.2 - Prob. 45E Ch. 9.2 - Prob. 46E Ch. 9.2 - Prob. 47E Ch. 9.2 - Prob. 48E Ch. 9.2 - Prob. 49E Ch. 9.2 - Prob. 50E Ch. 9.2 - Prob. 51E Ch. 9.2 - A string is wound around a circle and then unwound...Ch. 9.2 - A cow is tied to a silo with radius r by a rope...Ch. 9.3 - Prob. 1E Ch. 9.3 - Prob. 2E Ch. 9.3 - Prob. 3E Ch. 9.3 - Prob. 4E Ch. 9.3 - Prob. 5E Ch. 9.3 - Prob. 6E Ch. 9.3 - Prob. 7E Ch. 9.3 - Prob. 8E Ch. 9.3 - Prob. 9E Ch. 9.3 - Prob. 10E Ch. 9.3 - Prob. 11E Ch. 9.3 - Prob. 12E Ch. 9.3 - Identify the curve by finding a Cartesian equation...Ch. 9.3 - Identify the curve by finding a Cartesian equation...Ch. 9.3 - Identify the curve by finding a Cartesian equation...Ch. 9.3 - Prob. 16E Ch. 9.3 - Prob. 17E Ch. 9.3 - Prob. 18E Ch. 9.3 - Prob. 19E Ch. 9.3 - Prob. 20E Ch. 9.3 - Prob. 21E Ch. 9.3 - Prob. 22E Ch. 9.3 - Sketch the curve with the given polar equation by...Ch. 9.3 - Sketch the curve with the given polar equation by...Ch. 9.3 - Sketch the curve with the given polar equation by...Ch. 9.3 - 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Prob. 4E Ch. 9.5 - Prob. 7E Ch. 9.5 - Prob. 6E Ch. 9.5 - Prob. 5E Ch. 9.5 - Prob. 8E Ch. 9.5 - Prob. 9E Ch. 9.5 - Prob. 10E Ch. 9.5 - Prob. 11E Ch. 9.5 - Prob. 12E Ch. 9.5 - Prob. 13E Ch. 9.5 - Prob. 14E Ch. 9.5 - Prob. 15E Ch. 9.5 - Prob. 16E Ch. 9.5 - Prob. 17E Ch. 9.5 - Prob. 18E Ch. 9.5 - Prob. 19E Ch. 9.5 - Prob. 20E Ch. 9.5 - Prob. 21E Ch. 9.5 - Prob. 22E Ch. 9.5 - Prob. 23E Ch. 9.5 - Prob. 24E Ch. 9.5 - The orbit of Halleys comet, last seen in 1986 and...Ch. 9.5 - Prob. 26E Ch. 9.5 - Prob. 27E Ch. 9.5 - The distance from the dwarf planet Pluto to the...Ch. 9.5 - Prob. 29E Ch. 9 - Prob. 1RCC Ch. 9 - Prob. 2RCC Ch. 9 - Prob. 3RCC Ch. 9 - Prob. 4RCC Ch. 9 - Prob. 5RCC Ch. 9 - Prob. 6RCC Ch. 9 - Determine whether the statement is true or false....Ch. 9 - Prob. 2RQ Ch. 9 - Determine whether the statement is true or false....Ch. 9 - Prob. 4RQ Ch. 9 - Prob. 5RQ Ch. 9 - Prob. 6RQ Ch. 9 - Prob. 7RQ Ch. 9 - Prob. 8RQ Ch. 9 - Prob. 1RE Ch. 9 - Prob. 2RE Ch. 9 - Prob. 3RE Ch. 9 - Prob. 4RE Ch. 9 - 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The points of intersection of the curves r = cot θ and r = 2 cos θ .

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Chapter 9 Solutions