A cycloid is generated by and for

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

A cycloid is generated by x=t−sin⁡tx=t-\sin t and y=1−cos⁡ty=1-\cos t for t>0t>0. The tangent line at t=π/3t=\pi/3 is perpendicular to the tangent line at which of the following parameter values in the interval π<t<2π\pi < t < 2\pi? (a) 3π/23\pi/2 (b) π\pi (c) 4π/34\pi/3 (d) 5π/35\pi/3

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