Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

Show that the curve with parametric equations $ x = \sin t $, $ y = \cos t $, $ z = \sin^2 t $ is the curve of intersection of the surfaces $ z = x^2 $ and $ x^2 + y^2 = 1 $. Use this fact to help sketch the curve.

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Wen Zheng

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus 3

Chapter 13

Vector Functions

Section 1

Vector Functions and Space Curves

Johns Hopkins University

Campbell University

Baylor University

University of Michigan - Ann Arbor

Lectures

03:04

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x. The input of a function is called the argument and the output is called the value. The set of all permitted inputs is called the domain of the function. Similarly, the set of all permissible outputs is called the codomain. The most common symbols used to represent functions in mathematics are f and g. The set of all possible values of a function is called the image of the function, while the set of all functions from a set "A" to a set "B" is called the set of "B"-valued functions or the function space "B"["A"].

08:32

In mathematics, vector calculus is an important part of differential geometry, together with differential topology and differential geometry. It is also a tool used in many parts of physics. It is a collection of techniques to describe and study the properties of vector fields. It is a broad and deep subject that involves many different mathematical techniques.

11:26

Show that the curve with p…

02:42

03:20

Exercise 2 Show that the c…

02:10

05:30

The problem is show that is a curve for its parametric equations x. Equal to sine t y is equal to sine t. 3 is equal to sine t square is a curve of intersection of the surfaces 3 equal to x, squared and x, squared plus y squared is equal to 1. I use this fact to help sketch the curve. So first the relation between x and wat and z have x is sin is equal to sine square, so we have is equal to x, coined and x. Squared plus y squared is equal to sine t square plus sine t square, so this is equal to 1. So behalf, the curve is a curve of intersection of the surfaces equal to x, squared and x, squared plus y squared equals to 1 point now. Let'S sketch the curve, the first we draw the sin or x, squared plus y squared is equal to 1, and then we choose some points on the curve, so 0100 negative, 10 and 101 negative 101 at the point of 101. Is this point and 0 negative 10? This point and 101 is this point and 1 negative 10 poison. The graph is like this is a graph of the.

View More Answers From This Book

Find Another Textbook

01:38

the radius of a cone is 7 cm and its slant height is 10 centimetre calculate…

02:21

What's the lcm of 510 and 92 show with steps

00:43

what is the passing criteria of cbse class 10th ?I want to ask about the che…

00:46

2.24689 express as a rational number in the form of p/q?

01:58

A die is rolled 200 times with the following results. Outcome 1 2 3 4 5 6 Fr…

01:19

A rectangle has an area of 18cm2 the legnths of the sides are whole number. …

00:34

Mother cut a sheet of paper into 10 pieces. She then took one piece of it an…

04:35

A plate of cakes holds 12 different cakes. Find the number of ways these cak…

01:09

A shopkeeper purchased 124 pencils at the rate rupees 4 and sold them at ru…

02:30

A machine manufacturers 23875 screws per day. How many screws did it produce…