A curve is described by the parametric equations x=5 t

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

A curve is described by the parametric equations x=5cos⁡t,y=4sin⁡t−sin⁡2t,x=5\cos t,\qquad y=4\sin t-\sin 2t, with 0≤t≤2π0\le t\le 2\pi. (i) Find all values of tt in the stated interval for which the tangent to the curve is horizontal. (ii) Write the coordinates of every point on the curve where a horizontal tangent occurs. (iii) How many distinct horizontal tangents does the curve possess in the interval 0≤t≤2π0\le t\le 2\pi? Give reasons for your answer.

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