Question

if x=a(t+sint),y=a(1-cost) if dx/dy=cotp find p​

Answer 1

Answer:

$x = a(t + \sin(t) ) \\ \frac{dx}{dt} = a (1 + \cos(t) ) \\ y = a(1 - \cos(t) ) \\ \frac{dy}{dt} = a( \sin(t) ) \\ hence \\ \frac{dx}{dy} = \frac{dx}{dt} \times \frac{dt}{dy} \\ \cot(p) = \frac{a(1 + \cos(t) }{a( \sin(t) )} \\ \cot(p) = \frac{1 + \cos(t) }{ \sin(t) } \\ \cot(p) = \frac{2 { \cos( \frac{t}{2} ) }^{2} }{2 \sin( \frac{t}{2} ) \cos( \frac{t}{2} ) } \\ \cot(p) \: = \cot( \frac{t}{2} ) \\ hence \: \\ p = \frac{t}{2}$