A curve $C$ has parametric equations $x={{\sin }^{2}} heta $, $y=2\sin heta -{{\sin }^{3}} heta

Question

A curve $C$ has parametric equations $x={{\sin }^{2}}	heta $, $y=2\sin 	heta -{{\sin }^{3}}	heta $, where $-\frac{\pi }{2}\le 	heta \le \frac{\pi }{2}$. Find the value(s) of the parameter $	heta$ at the point(s) where the curve $C$ is stationary. [4] Show that the equation of the tangent to the curve at the point where the gradient is $\frac{5}{4}$ is given by $y=\frac{5}{4}x+\frac{9}{16}$. [4] Determine whether the tangent $y=\frac{5}{4}x+\frac{9}{16}$ meets the curve $C$ again. [3]

Accepted Answer

$y = \frac{5}{4}x + \frac{9}{16}$

2016 MI P1 Q11

2016 MI P1 Q11

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