Consider the curve represented by the parametric equations x(t)= 2+sin(t) and y(t)=1-cos(t) when answering the following questions.

Question

A) Find Dy/Dx in terms of t

B) Find all values of t where the curve has a horizontal tangent.

C) Find all values of t where the curve has a vertical tangent.

D) Write an integral that represents the arc length of the curve on the interval 0 ≤ t ≤ 2π. Evaluate the integral.

Answer 1

Just plug and chug.
A) dy/dx = (dy/dt) / (dx/dt) = sin(t)/cos(t) = tan(t)

B and C should now be clear

Now you can easily write the arc length integral in terms of t - it might surprise you.

Answer 2

So the answer to B is t=+- (pi)(n)
and for C it is (pi/2)(+-)(pi)(n)