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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.

1.

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

(a)

To determine

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

and r<0 .

Explanation

Given:

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

(1,π4) .

Calculation:

The polar coordinate (r,θ)

(1,π4)

Angle θ=π4 is positive and measured in the counter clockwise direction, so θ lies on the positive y axis, and radius r=1 is positive.

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

The coordinate pair of (1,π4) for the condition r>0 is (r,θ+2π) .

Substitute π4 for θ and 1 for r in polar coordinate (r,θ+2π)

(1,π4+2π)(1,9π4)

The other coordinate pair for the condition r>0 is (1,9π4)

(b)

To determine

To plot: The polar coordinate (2,3π2) and find the other pairs for the conditions r>0

and r<0 .

(c)

To determine

To plot: The polar coordinate (3,π3) and find the other pairs for the conditions r>0

and r<0 .

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P-52RECh-10 P-53RECh-10 P-54RECh-10 P-55RECh-10 P-56RECh-10 P-57RECh-10 P-58RECh-10 P-1PCh-10 P-2PCh-10 P-3PCh-10 P-4PCh-10 P-5PCh-10 P-6P

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