   Chapter 13.1, Problem 27E

Chapter
Section
Textbook Problem

# Show that the curve with parametric equations x = t cos t, y = t sin t, z = t lies on the cone z2 = x2 + y2, and use this fact to help sketch the curve.

To determine

To show: The curve with parametric equations x=tcost , y=tsint , and z=t lies on a cone z2=x2+y2 and sketch the curve.

Explanation

Given data:

The parametric equation is x=tcost , y=tsint , and z=t .

Find the value of x2+y2 .

x2+y2=(tcost)2+(tsint)2=t2cos2t+t2sin2t=t2(cos2t+sin2t)=t2(1){cos2x

### 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

#### The difference between population variance and sample variance.

Statistics for The Behavioral Sciences (MindTap Course List)

#### In Exercises 23-36, find the domain of the function. 24. f(x) = 7 x2

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### True or False: , for –π ≤ t ≤ π, is smooth.

Study Guide for Stewart's Multivariable Calculus, 8th

#### 0 1 does not exist

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 