Consider the polar curves C1 : r = 4 + (3√2)/(2) cos θ and C2 : r = 2 − (√2)/(2) cos θ as shown in the figure on the right. The curves C1 and C2 are both symmetric with respect to the polar axis. Each of these curves is traced counterclockwise as the value of θ increases on the interval [0, 2π]. Also, for each of these curves, r > 0 when θ ∈ [0, 2π]. Let P be the point of intersection of C1 and C2 in the second quadrant. Find polar coordinates (r, θ) for the point P where r > 0 and θ ∈ [0, 2π].

Consider the polar curves C1 : r = 4 + (3√2)/(2) cos θ and C2 : r = 2 − (√2)/(2) cos θ as shown in the figure on the right. The curves C1 and C2 are both symmetric with respect to the polar axis. Each of these curves is traced counterclockwise as the value of θ increases on the interval [0, 2π]. Also, for each of these curves, r > 0 when θ ∈ [0, 2π]. Let P be the point of intersection of C1 and C2 in the second quadrant. Find polar coordinates (r, θ) for the point P where r > 0 and θ ∈ [0, 2π].

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.4: Complex Numbers

Problem 42E

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Question

Consider the polar curves C₁ : r = 4 + (3√2)/(2) cos θ and C₂ : r = 2 − (√2)/(2) cos θ as shown in the figure on the right. The curves C₁ and C₂ are both symmetric with respect to the polar axis. Each of these curves is traced counterclockwise as the value of θ increases on the interval [0, 2π].

Also, for each of these curves, r > 0 when θ ∈ [0, 2π].

Let P be the point of intersection of C₁and C₂ in the second quadrant. Find polar coordinates (r, θ) for the point P where r > 0 and θ ∈ [0, 2π].