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.

a. once clockwise.

b. once counterclockwise.

c. three times clockwise.

d. three times counterclockwise.

a)

b)

c)

d)

Step-by-step explanation:

The parametric equation for a circle is:

Where a is the radius and b is the angular displacement.

a) If a is negative in y and 0 ≤ b ≤ 2π, we have clockwise moves.

b)  If a is positive in y and 0 ≤ b ≤ 2π, we have counterclockwise moves.

c) If a is negative in y and 0 ≤ b ≤ 6π, we have three times clockwise moves.

d) If a is positive in y and 0 ≤ b ≤ 6π, we have three times counterclockwise moves.

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1. 3

2. 4

3. 1

hope this ! have a great day.

-wfz