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

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.

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2 answers
  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.

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

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