Question

A particle simultaneously participates in two mutually perpendicular oscillations $x=sin\pi t$ & $y=2cos2\pi t$. Write the equation of trajectory of the particle.

Answer 1

$x=\sin \pi ty=2\cos 2\pi t$

As we know

$\cos 2\theta =1-2{\sin }^2\theta$

So,

$y=2(1-2{\sin }^2\pi t)y=2(1-2x^2)y=2-4x^2$