hexacordoK

2021-08-22

The position of an object in circular motion is modeled by the parametric equations $x=3\mathrm{sin}2t$ $y=3\mathrm{cos}2t$ where t is measured in seconds.

Outline the trajectory of the object by providing the radius of the circle, the location at time t = 0, the direction of motion (clockwise or counterclockwise), and the time t it takes to complete one cycle around the circle.

Willie

Skilled2021-08-23Added 95 answers

The data in the question indicates that

$x=2\mathrm{sin}t$

$y=2\mathrm{cos}t$

The radius of a circle can be calculated using the following formula:

$r=\sqrt{{a}^{2}+{b}^{2}}$

$r=\sqrt{{\left(2\mathrm{sin}t\right)}^{2}+\left(2{\mathrm{cos}t}^{2}\right)}$

$r=\sqrt{4{\mathrm{sin}}^{2}t+4{\mathrm{cos}}^{2}t}$

Using trigonometric identity,

${\mathrm{cos}}^{2}t+4{\mathrm{sin}}^{2}t=1$

$r=4\cdot 1$

r=2 unit

Motion= clock wise

the time for complete $1=2\pi =2\cdot 3.14=6.28$

$.:t=6.28$

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