A particle moves in $x-y$ plane according to rule $x=a \sin \omega t$ and $y=a \cos \omega t$. The p

Question

A particle moves in $x-y$ plane according to rule $x=a \sin \omega t$ and $y=a \cos \omega t$. The particle follows\

Professor PC Thomas Classes · Answer

(b) : $x=a \sin \omega t$ or $\frac{x}{a}=\sin \omega t$\ $y=a \cos \omega t$ or $\frac{y}{a}=\cos \omega t$\ Squaring and adding, we get\ $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{a^{2}}=1 \quad\left(\because \cos ^{2} \omega t+\sin ^{2} \omega t=1ight)$\ or $x^{2}+y^{2}=a^{2}$\ This is the equation of a circle. Hence particle follows a circular path.\