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The position of an object in circular motion is modeled by the given parametric equations. Describe the path of the object by stating the radius of the circle, the position at time t = 0, the orientation of the motion (clockwise or counterclockwise), and the time t that it takes to complete one revolution around the circle.
x = 4 cos 3t, y = 4 sin 3t
How do you get to that solution?

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Answer:

4 units ; counter clockwise ; 2.09 units

Step-by-step explanation:

Given the following :

x = 4 cos 3t

y = 4 sin 3t

The Radius (r) could be obtained using Pythagoras:

R = √(x^2 + y^2)

R = √[(4cos3t)^2 + (4sin3t)^2]

R = √[16cos^(2)3t + 16sin^(2)3t]

Recall : cos^2θ + sin^2θ = 1

Therefore, cos^(2)3t + sin^(2)3t= 1

Where, 3t stands for θ

R = √[16cos^(2)3t + 16sin^(2)3t]

Factorizing:

R = √16[cos^(2)3t + sin^(2)3t)]

R = √16[1]

R = √16

R = 4 units

Position at time t = 0

x = 4 cos 3(0)

x = 4 cos 0

x = 4 * 1 = 4 units

y = 4 sin 3t

y = 4 sin 3(0)

y = 4 * sin 0

y = 0

Position at t = 0;

(x, y) = (4, 0) = counterclockwise

Time taken to complete 1 complete revolution:

2Ï€/3 = 6.2831853 /3 = 2.0943951

= 2.09