The position of an object in circular motion is modeled by the parametric equations x =

The position of an object in circular motion is modeled by the parametric equations $$\displaystyle{x}={3}{\sin{{2}}}{t}$$ $$\displaystyle{y}={3}{\cos{{2}}}{t}$$ where t is measured in seconds.
Describe the path of the object by stating the radius of the circle, the position at time t = 0, the orientation of motion (clockwise or counterclockwise), and the time t it takes to complete one revolution around the circle.

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Willie

According to given data in the question
$$\displaystyle{x}={2}{\sin{{t}}}$$
$$\displaystyle{y}={2}{\cos{{t}}}$$
We know the formula for a radius of a circle
$$\displaystyle{r}=\sqrt{{{a}^{{2}}+{b}^{{2}}}}$$
$$\displaystyle{r}=\sqrt{{{\left({2}{\sin{{t}}}\right)}^{{2}}+{\left({2}{\cos{{t}}}^{{2}}\right)}}}$$
$$\displaystyle{r}=\sqrt{{{4}{{\sin}^{{2}}{t}}+{4}{{\cos}^{{2}}{t}}}}$$
Using trigonometric identity,
$$\displaystyle{{\cos}^{{2}}{t}}+{4}{{\sin}^{{2}}{t}}={1}$$
$$\displaystyle{r}={4}\cdot{1}$$
r=2 unit
Motion= clock wise
the time for complete $$\displaystyle{1}={2}\pi={2}\cdot{3.14}={6.28}$$
$$\displaystyle.:{t}={6.28}$$