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karush

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11.1 Parametric equations and a parameter interval for the motion of a particle in the xy-plane given. Identify the paritcals path by finding a Cartestian equation for it $x=2\cos t, \quad 2 \sin t, \quad \pi\le t \le 2\pi$

(a) Identify the particles path by finding a Cartesian Equation the Cartesian equation is

$$x^2+y^2=4$$

(b) Indicate the portion of the graph traced by the particle and the direction of motion

so if $x=2cos{(\pi)}=-2$ and $x=2cos{(2\pi)}=2$ then

$$-2\le t \le 2$$

and the particle moves in a clockwise direction

View attachment 9217

ok, I think this is correct but I got the carresian equation just by ploting the parametric into desmos and saw that it was a circle with a radius of 2. the examples didn't the normal steps

also obviously I just pluged into see the direction of motion so...

I was going to try to use tikx on this but didn't how to use an interval be cute to put an arrow also

(a) Identify the particles path by finding a Cartesian Equation the Cartesian equation is

$$x^2+y^2=4$$

(b) Indicate the portion of the graph traced by the particle and the direction of motion

so if $x=2cos{(\pi)}=-2$ and $x=2cos{(2\pi)}=2$ then

$$-2\le t \le 2$$

and the particle moves in a clockwise direction

View attachment 9217

ok, I think this is correct but I got the carresian equation just by ploting the parametric into desmos and saw that it was a circle with a radius of 2. the examples didn't the normal steps

also obviously I just pluged into see the direction of motion so...

I was going to try to use tikx on this but didn't how to use an interval be cute to put an arrow also