Question

A particle moves in x-y plane according to rule x=asinwt and y=acoswt.The particle follows..
1.an elliphtical path
2.a circular path
3.a parabolic path
4.a straight line path inclined equally to x and y-axes

Answer 1

hint

isolate expressions for sin wt and cos wt and then use a well known trig identity to connect x and y

Answer 2

hint:
the equations provided:
\[\begin{gathered}
x\left( t \right) = a\sin \left( {\omega t} \right) \hfill \\
y\left( t \right) = a\cos \left( {\omega t} \right) \hfill \\
\end{gathered} \]
are the parametric equations of a circumference, please note that:
\[{x^2} + {y^2} = {\left\{ {a\sin \left( {\omega t} \right)} \right\}^2} + {\left\{ {a\cos \left( {\omega t} \right)} \right\}^2} = {a^2}\]

Answer 3

how do u no tht its a eqaution of circle....since its nt mentioned ,can i take it for parabolla???

Answer 4

nah

it's a circle:-)

Answer 5

the equation above:
\[{x^2} + {y^2} = {a^2}\]
is, in the plane \((x,y)\), the equation of a circumference centered at the origin, and whose radius is \(a\), namely: