`" The area between the cycloid "x=a(theta-sin theta),y=a(1-cos theta),0<=theta<2 pi" and the "x-" axis is "`

If x=-a(theta-sin theta),y=a(1-cos theta), then (dy)/(dx) is

If 2 theta is an acute angle, then the acute angle between the two lines x^(2)(cos theta-sin theta)+2xy.cos theta +y^(2)(cos theta +sin theta)=0 is

cos theta/(1+sin theta)=(1-sin theta)/cos theta

The normal to the curve x=a(cos theta-theta sin theta),y=a(sin theta-theta cos theta) at any point,theta, is such that

The normal to the curve x=a(cos theta + theta sin theta), y=a(sin theta - theta cos theta) at any theta is such that

If the angle theta is acute, then the acute angle between x^(2)(cos theta-sin theta)+2xy cos theta+y^(2)(cos theta+sin theta)=0, is

What is the distance between the points A(sin theta-cos theta,0) and B(0,sin theta+cos theta)?

If x=a ( theta -sin theta ) ,y=a(1-cos theta ) ,then (dy)/(dx) =