   Chapter 10.3, Problem 91E

Chapter
Section
Textbook Problem

Cycloid Use the parametric equations x = a ( θ − sin )   and   y = a ( 1 − cos θ ) ,     a > 0 to answer the following.(a) Find d y / d x and d 2 y / d x 2 .(b) Find the equation of the tangent line at the point where θ = π / 6 (c) Find all points of horizontal tangency.(d) Determine where the curve is concave upward or concave downward.(e) Find the length of one arc of the curve.

(a)

To determine

To calculate: dydx and d2ydx2 for x=a(θsinθ) and y=a(1cosθ) and a>0

Explanation

Given: x=a(θsinθ) and y=a(1cosθ) and a>0

Calculation:

Differentiation above equation with respect to θ

dxdθ=a(1cosθ) and dydθ=asinθ

dydx=dydθdxdθ=asinθa(1cosθ)=sinθ(1cos

(b)

To determine

To calculate: Equation of tangent line at the point where θ=π6

(c)

To determine

To calculate: All point of horizontal tangency

(d)

To determine
Where curve is concave upward or downward

(e)

To determine

To calculate: Length of one arc of curve

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Solve the following problems and reduce to lowest terms. 13.

Contemporary Mathematics for Business & Consumers

Given: ABDCABDC C is the midpoint of BE Prove: ACDE

Elementary Geometry For College Students, 7e

Solve each equation: 4x=60

Elementary Technical Mathematics

Study Guide for Stewart's Multivariable Calculus, 8th 