Use the parametric equations x a( sin) and y a(1 cos ), a 0 to answer the following (a) Find dy dx and d 2 y dx 2 (b) Find the equation of the tangent line at the point where 6 (c) Find all points of horizontal tangency (d) Determine where the curve is concave upward or concave downward (e) Find the length of one arc of the curve

Question: Use the parametric equations x = a( - sin) and y = a(1 - cos ), a > 0 to answer the following. (a) Find

Use the parametric equations x = a(θ - sinθ) and y = a(1 - cos θ), a > 0 to answer the following.
(a) Find dy/dx and d²y/dx².
(b) Find the equation of the tangent line at the point where θ = π/6.
(c) Find all points of horizontal tangency.
(d) Determine where the curve is concave upward or concave downward.
(e) Find the length of one arc of the curve.

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