Question

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

Answer 1

Answer:

cot⁻¹ [ a ( 1 + cos t ) / ( sin t ) ]

Step-by-step explanation:

Given :

x = a ( t + sin t )

= > x = a t + a sin t

Diff. w.r.t. t :

d x / d t = a ( t )' + a ( sin t )'

= > d x / d t = a + a cos t

= > d x / d t = a ( 1 + cos t )

Also given :

y = ( 1 - cos t )

Diff. w.r.t. t :

= > d y / d t = ( 1 )' - ( cos t )'

= > d y / d t = - ( - sin t )

= > d y / d t = sin t

Now as we do in parametric function :

d x / d y = ( d x / d t ) / ( d y / d t )

= > d x / d y = a ( 1 + cos t ) / ( sin t )

Given d x / d y = cot P

cot P = a ( 1 + cos t ) / ( sin t )

P = cot⁻¹ [ a ( 1 + cos t ) / ( sin t ) ]

Hence we get required answer.