Question

If $x=10(t-\sin t),y=12(1-\cos t),$ find $\frac{dy}{dx}.$

Answer 1

$x=10(t-\sin t)$

Differentiating w.r.t. t, we get,

$\frac{dx}{dt}=10(1-\cos t)$

$y=12(1-\cos t)$

Differentiating w.r.t. t, we get,

$\frac{dy}{dt}=12\sin t$

Thus, $\frac{dy}{dx}=\frac{12\sin t}{10(1-\cos t)}$

$\frac{dy}{dx}=\frac{6\sin t}{5(1-\cos t)}$