For the cycloidal curve

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

Problem

For the cycloidal curve x=a (t+sin⁡t),  y=a (1−cos⁡t)x=a\,(t+\sin t),\;y=a\,(1-\cos t), obtain the equation of the tangent at t=π2t=\dfrac{\pi}{2} in a form that does not contain the parameter tt. (a) x+y−aπ2=0x+y-\dfrac{a\pi}{2}=0 (b) x−y−aπ2=0x-y-\dfrac{a\pi}{2}=0 (c) x−y+aπ2=0x-y+\dfrac{a\pi}{2}=0 (d) x−y−a=0x-y-a=0

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