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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates of this point, one with r > 0 and one with r < 0.

2.

  1. (a) (2, 5π/6)
  2. (b) (1, −2π/3)
  3. (c) (−1, 5π/4)

(a)

To determine

To plot: The polar coordinate (2,5π6) and find the other pairs for the conditions r>0

and r<0 .

Explanation

Given:

The polar coordinate (r,θ) is as below.

(2,5π6) .

Calculation:

The polar coordinate (r,θ)

(2,5π6)

Angle θ=5π6 is positive and measured in the counter clockwise direction, so θ lies on the positive y axis, and radius r=2 is positive.

The polar coordinate system for the conditions r>0 and r<0 .

The coordinate pair of (2,5π6) for the condition r>0 is (r,θ+2π) .

Substitute 5π6 for θ and 2 for r in polar coordinate (r,θ+2π)

(2,5π6+2π)(2,17π6)

The other coordinate pair for the condition r>0 is (2,17π6)

(b)

To determine

To plot: The polar coordinate (1,2π3) and find the other pairs for the conditions r>0

and r<0 .

(c)

To determine

To plot: The polar coordinate (1,5π4) and find the other pairs for the conditions r>0

and r<0 .

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