Chapter 9: Q. 3 (page 774)

Sketching parametric equations: Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.
$x = \sin t$ , $y = \cos t$ , $t \in [0, 4 π]$ .

Short Answer

Expert verified

The graph is circle in clockwise.

Step by step solution

Step 1. Given Information.

The equations are $x = \sin t$ and $y = \cos t$ such that $t \in [0, 4 π]$ .

Step 2. Explanation.

Start by eliminating the parameter. Square the equations for x and y,

So,

$x^{2} = \sin^{2} t$

$y^{2} = \cos^{2} t$

Apply the Pythagorean identity.

$\sin^{2} t + \cos^{2} t = 1$

So, $x^{2} + y^{2} = 1$

So, this is a circle of radius 1 and centered at the origin.

Step 3. Calculation

To know the direction make a table as follows,

t	0	$π$	$2 π$	$4 π$
$x = \sin t$	$\sin 0 = 0$	$sinπ = 0$	$\sin 2 π = 0$	$\sin 4 π = 0$
$y = \cos t$	$\cos 0 = 1$	$cosπ = - 1$	$\cos 2 π = 1$	$\cos 4 π = 1$

Draw the graph as follows,

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Sketching parametric equations: Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.
$x = \sin t$ , $y = \cos t$ , $t \in [0, 4 π]$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Discrete Mathematics

Applied Mathematics

Logic and Functions

Calculus

Study anywhere. Anytime. Across all devices.

Sketching parametric equations: Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.x=sint,y=cost,t∈0,4π.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Discrete Mathematics

Applied Mathematics

Logic and Functions

Calculus

Study anywhere. Anytime. Across all devices.

Sketching parametric equations: Sketch the curves defined by the given sets of parametric equations. Indicate the direction of motion on each curve.
$x = \sin t$ , $y = \cos t$ , $t \in [0, 4 π]$ .