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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

  1. (a) Find parametric equations for the set of all points P as shown in the figure such that |OP| = |AB|. (This curve is called the cissoid of Diodes after the Greek scholar Diodes, who introduced the cissoid as a graphical method for constructing the edge of a cube whose volume is twice that of a given cube.)
  2. (b) Use the geometric description of the curve to draw a rough sketch of the curve by hand. Check your work by using the parametric equations to graph the curve.

Chapter 10.1, Problem 44E, (a) Find parametric equations for the set of all points P as shown in the figure such that |OP| =

(a)

To determine

To find: The parametric equations. of all the set of points P .

Explanation

Given:

The curve Cissoid of Diocles is shown in below figure1.

Calculation:

Let θ be the angle of inclination of segment OP .

OB=2acosθ

The point of C be (2a,0) .

The right triangle OAC .

OA=2acosθ

OP=ABOP=OBOA

Substitute (2acosθ) for |OA| and (2acosθ) for |OB| in above equation

(b)

To determine

To plot: The curve using the parametric equations. x=2asin2θ and y=2asin2θtanθ .

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Chapter 10 Solutions

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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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