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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Plot the point whose polar coordinates are given. Then find the Cartesian coordinates of the point.

3.

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

(a)

To determine

To plot: The polar coordinate (2,3π2) and find the Cartesian coordinate of the point for the given polar coordinate.

Explanation

Given:

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

(2,3π2)

Calculation:

The polar coordinate (r,θ)

(2,3π2)

The equation for the variable x is given below,

x=rcosθ (1)

The equation for the variable y is given below,

y=rsinθ (2)

Substitute (π) for θ and (1) for r in equation (1),

x=rcosθ=(2)cos(3π

(b)

To determine

To plot: The polar coordinate (2,π4) and find the Cartesian coordinate of the point for the given polar coordinate.

(c)

To determine

To plot: The polar coordinate (1,π6) and find the Cartesian coordinate of the point for the given polar coordinate.

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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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