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kiki195ms

Answered question

2021-11-27

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

Forneadil

Beginner2021-11-28Added 18 answers

Step 1
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

(a, 0)

are

x = a \cos t

y = a \sin t

It requires going around a circle once.
Step 2
Therefore required parametric equations are

x = a \cos t, t = a \sin t

and

0 \leq t \leq 2 π

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