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

hexacordoK 2021-08-22 Answered
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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Expert Answer

Willie
Answered 2021-08-23 Author has 17229 answers

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 \(\displaystyle{1}={2}\pi={2}\cdot{3.14}={6.28}\)
\(\displaystyle.:{t}={6.28}\)

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