Question

Find $\frac{dy}{dx}$,if y=12(1-cost),x=10(t-sint),$-\frac{\pi}{2}$<t<$\frac{\pi}{2}$

Answer 1

It is given that ,y=12(1-cost),x=10(t-sint)
∴$\frac{dy}{dx}$=$\frac{d}{dt}$(10(t-sint))=10.$\frac{d}{dt}$(t-sint)=10(1-cost)
$\frac{dy}{dt}$=$\frac{d}{dt}$[12(1-cost)]=12.$\frac{d}{dt}$(1-cost)=12.[0-(-sint)]=12sint
∴$\frac{dy}{dt}$=$\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$ =$\frac{12sin\,t}{10(1-cos\,t)}$
=$\frac{12.2sin\frac{t}{2}cos\frac{t}{2}}{10.2sin\frac{2t}{2}}$=$\frac{6}{5}cot\frac{t}{2}$