Consider the parametric equation?

Question

Consider the parametric equation

x = 5 (cos O + O sin O)

y = 5 (sin O + O cos O)

What is the length of the curve for O = 0 to O = 3/10pi ?

What is the length of the curve for to ?

Answer 1

After a little research - see the link in the source list.  It looks like you the length would be the integral from 0 to 3/10pi of

square root of ( (dx/dt)^2 + (dy/dt)^2))  dt

So you will need to take the derivative of each equation:

x = 5 (cos O + O sin O)  becomes

dx/dO = 5( -sin(O) + sin(O) + O cos(O)) = 5 O cos(O)

dy/dO = 5( cos(O) + cos(O) - O sin(O)) = 5 ( 2 cos(O) - O sin(O))

I am not going to do all the work for you but this should get you started.  See the reference and the equation about half-way down the page.  I am hoping that after squaring the dx/dO and dy/dO and adding them that things will cancel to make your problem simpler.