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
hint isolate expressions for sin wt and cos wt and then use a well known trig identity to connect x and y
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: \[{x^2} + {y^2} = {\left\{ {a\sin \left( {\omega t} \right)} \right\}^2} + {\left\{ {a\cos \left( {\omega t} \right)} \right\}^2} = {a^2}\]
how do u no tht its a eqaution of circle....since its nt mentioned ,can i take it for parabolla???
nah it's a circle:-)
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: |dw:1458300353885:dw|
Join our real-time social learning platform and learn together with your friends!