Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Use one of the formulas in (5) to find the area under one arch of the cycloid x = t - sint and y = 1 - cost. Work seen below.

Use one of the formulas in (5) to find the area under one arch of the cycloid x = t - sint and y = 1 - cost. Work seen below.

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.6: Parametric Equations
Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...
See similar textbooks
icon
Related questions
Question

Use one of the formulas in (5) to find the area under one arch of the cycloid  x = t - sint and y = 1 - cost. Work seen below.

How were the parametric equations x = 2pi - t (3) and y = 0 (4) found? This is an explanation of the problem but the work is not 100% clear.

Parametric equations are x = t - sin t and y = 1 − cost. Consider a curve C₁,0 ≤ t ≤ 2 as arch of the cycloid from (0, 0) to (2л, 0) with parametric equations x = t - sint (1) y = 1 - cost (2) Differentiate equation (1) with respect to t. (x) = 4(1-sin 1) dx = 4(1)-(sin t) dt dx dt dx = (1 cos t) dt Differentiate equation (2) with respect to t. (v) = (1 - cost) dt (1) - (cost) dy dt dy dt = 1 - cost dy = 0 - (- sin t) { (1) = 1, (sin t) = cos t} = {•: (k) = 0, & (cos t) = dt - sin t} sin tdt Consider a curve С₂,0 ≤ t ≤ 2л as a segment from (2л, 0) to (0, 0) with parametric equations x = 2л - t (3) y = 0 (4) ==
Transcribed Image Text:Parametric equations are x = t - sin t and y = 1 − cost. Consider a curve C₁,0 ≤ t ≤ 2 as arch of the cycloid from (0, 0) to (2л, 0) with parametric equations x = t - sint (1) y = 1 - cost (2) Differentiate equation (1) with respect to t. (x) = 4(1-sin 1) dx = 4(1)-(sin t) dt dx dt dx = (1 cos t) dt Differentiate equation (2) with respect to t. (v) = (1 - cost) dt (1) - (cost) dy dt dy dt = 1 - cost dy = 0 - (- sin t) { (1) = 1, (sin t) = cos t} = {•: (k) = 0, & (cos t) = dt - sin t} sin tdt Consider a curve С₂,0 ≤ t ≤ 2л as a segment from (2л, 0) to (0, 0) with parametric equations x = 2л - t (3) y = 0 (4) ==
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS