SOLUTION: Hi Please can somebody help with this problem i) The variables x and y are given in terms of the parameter t as x = 3t(1 + t^3) and y = 3t^2(1 + t^3). Prove that dy/dx

Question 373946: Hi
Please can somebody help with this problem
i) The variables x and y are given in terms of the parameter t as x = 3t(1 + t^3) and y = 3t^2(1 + t^3). Prove
that
dy/dx = t(2 + 5t^3)/1 + 4t^3
ii) A cycloid is a curve traced out by a point on the rim of a wheel as it rolls along the ground. Its curve may
be given parametrically by x = a(t - sin t) and y = a(1 - cos t), where a is a constant. Show that
dy/dx = cot(t/2)
Thanks
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
i) The variables x and y are given in terms of the parameter t as x = 3t(1 + t^3) and y = 3t^2(1 + t^3). Prove
that
dy/dx = t(2 + 5t^3)/1 + 4t^3
Find dy/dt and dx/dt
Divide dy/dt by dx/dt, you'll see that's what it is.
----------------
ii) A cycloid is a curve traced out by a point on the rim of a wheel as it rolls along the ground. Its curve may
be given parametrically by x = a(t - sin t) and y = a(1 - cos t), where a is a constant. Show that
dy/dx = cot(t/2)
dy/dt = asin(t)
dx/dt = a(1 - cos(t))
dy/dx = sin(t)/(1 - cos(t))
-------------------------
Use half-angle formula for cot(t/2)

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