Question

Find the parametric equations and a parameter interval for the motion of a particle that starts out at (a,0) and traces the x^2+y^2=a^2

a.once clockwise
b. once counter clockwise

Answer 1

a.\[x=a\cos{t}\quad y=-a\sin{t}\quad ,t\in(0,2\pi)\]
b.\[x=a\cos{t}\quad y=a\sin{t}\quad ,t\in(0,2\pi)\]

Answer 2

but how do you get that?

Answer 3

lke how do you solve for it?

Answer 4

\[x^2+y^2=a^2=a^2\cos^2{t}+a^2\sin^2{t}\quad,\quad a>0\]\[x=\pm a\cos{t}\quad,\quad y=\pm a\sin{t}\]\[x(t=0)=a\quad\Rightarrow\quad x=a\cos{t}\]\[\mbox{clockwise: } y=-a\sin{t}\]\[\mbox{counterclockwise: } y=+a\sin{t}\]

Answer 5

how come there is an a^2 infront of the sin and cos