Question

Find parametric equations and a parameter interval for the motion of a particle that starts at and traces the circle a. once clockwise. b. once counterclockwise. c. clockwise. d. counterclockwise.

Answer 1

The parametric equation are x = a cost and y = a sint and moves in counterclockwise direction.

According to the statement

we have given that the Find parametric equations and a parameter interval for the motion of a particle that starts at (a,0) and traces the circle $x^{2} + y^{2} = a^{2}$ once counterclockwise.

And we have to find the parametric equation for this given statement.

So,

A parametric equation defines a group of quantities as functions of one or more independent variables called parameters.

Then

A particle that starts at (a,0) and traces the circle $x^{2} + y^{2} = a^{2}$ once counterclockwise.

The parametric equations for a circle $x^{2} + y^{2} = a^{2}$ and stats at (a,0) are

x = a cost

y = a sint

It requires going around a circle once.

Therefore required parametric equations are x = a cost and y = a sint and

$0\leq t\leq 2\pi$.

So, The parametric equation are x = a cost and y = a sint and moves in counterclockwise direction.

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Question:

Find parametric equations and a parameter interval for the motion of a particle that starts at (a,0) and traces the circle $x^{2} + y^{2} = a^{2}$ once counterclockwise.

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