Explanation Given: r ( t ) = 〈 cos 2 t sin t , sin 2 t , cos 2 t cos t 〉 Radius of sphere = 1. Center of sphere = (0,0,0) Formula used: General equation of sphere is ( x − a ) 2 + ( y − b ) 2 + ( z − c ) 2 = r 2 , Where a,b,c is center of sphere and r is radius of sphere. sin 2 x + cos 2 x = 1 Calculation: First we will find equation of sphere: ( x − a ) 2 + ( y − b ) 2 + ( z − c ) 2 = r 2 ⇒ ( x − 0 ) 2 + ( y − 0 ) 2 + ( z − 0 ) 2 = ( 1 ) 2 ⇒ x 2 + y 2 + z 2 = 1 r ( t ) = 〈 cos 2 t sin t , sin 2 t , cos 2 t cos t 〉 ⇒ x = cos 2 t sin t ⇒ y = sin 2 t ⇒ z = cos 2 t cos t To show that curve lies on the sphere, we will substitute the coordinates of curve in sphere. If we get value as 0, then we can confirm that the curve lies on the sphere To determine (b) Show that curve intersects the x-axis, the y-axis, and the z-axis.

4th Edition

ISBN: 9781319279813

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Concept explainers

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magn…

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.

Question

Chapter 13.1, Problem 23E

To determine

(a)

Show that curve r(t)=〈cos2tsint,sin2t,cos2tcost〉 lies on the sphere of radius 1 centered at the origin.

To determine

(b)

Show that curve intersects the x-axis, the y-axis, and the z-axis.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.1, Problem 22E

Chapter 13.1, Problem 24E

Students have asked these similar questions

x The function f is shown below. If I is the function defined by g(x) = √ ƒ(t) dt, find the value of g"(-8) in simplest form. g -1 8 y 7 10 6 LC 5 4 3 2 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 -1 -2 -3 -4 -5 56 -6 -7 -8 4 5 Graph of f 10 6 00 7 8 9 10 x

The function f is shown below. If g is an antiderivative of f such that g(6) = 2, what is the maximum value of g on the closed interval [-9,9]? 8 7 6 Сл 5 4 3 1 y Graph of f -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 23 4 -1 -2 -3 -4 -6 56 -5 -7 -8 LO 5 9 7 8 9 10

x The function of is shown below. If I is the function defined by g(x) = [* f(t)dt, write the equation of the line tangent to the graph of 9 at x = -3. g y Graph of f 8 7 6 5 4 32 1 x -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 56 -6 -7 -8

Chapter 13 Solutions

CALCULUS:EARLY TRANS.-SAPLINGPLUS

Ch. 13.1 - Prob. 1PQ Ch. 13.1 - Prob. 2PQ Ch. 13.1 - Prob. 3PQ Ch. 13.1 - Prob. 4PQ Ch. 13.1 - Prob. 5PQ Ch. 13.1 - Prob. 6PQ Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

(a) Show that curve r ( t ) = 〈 cos 2 t sin t , sin 2 t , cos 2 t cos t 〉 lies on the sphere of radius 1 centered at the origin.

Solution Summary: The author explains the equation of sphere: r(t)=langle mathrmcos2t, centered at the origin.

Concept explainers

(a)

Show that curve r(t)=〈cos2tsint,sin2t,cos2tcost〉 lies on the sphere of radius 1 centered at the origin.

(b)

Show that curve intersects the x-axis, the y-axis, and the z-axis.

Want to see the full answer?

Chapter 13 Solutions

(a) Show that curve r ( t ) = 〈 cos 2 t sin t , sin 2 t , cos 2 t cos t 〉 lies on the sphere of radius 1 centered at the origin.

Solution Summary: The author explains the equation of sphere: r(t)=langle mathrmcos2t, centered at the origin.

Concept explainers

(a) Show that curve r(t)=〈cos2tsint,sin2t,cos2tcost〉 lies on the sphere of radius 1 centered at the origin.

(b) Show that curve intersects the x-axis, the y-axis, and the z-axis.

Want to see the full answer?

Chapter 13 Solutions

(a)

Show that curve r(t)=〈cos2tsint,sin2t,cos2tcost〉 lies on the sphere of radius 1 centered at the origin.

(b)

Show that curve intersects the x-axis, the y-axis, and the z-axis.