The curve $C$ has parametric equations $x=a\sin t,\qquad y=a\sin t\cos t,$ for \(0\leq t&lt

Question

The curve $C$ has parametric equations $x=a\sin t,\qquad y=a\sin t\cos t,$ for $0\leq t<\pi$ and $a$ is a positive constant. Sketch the graph of $C$, stating clearly the coordinates of the points where the curve $C$ meets the axes.[2] State the equation of the line of symmetry.[1] Find the equation(s) of the tangent to $C$ which is parallel to the $x$-axis.[3] The tangent and normal to $C$ at the point $P$ where $t=\frac\pi6$ cut the $x$-axis at points $Q$ and $R$ respectively. Find the exact area of triangle $PQR$.[4]

Accepted Answer

(a) $(0,0),(a,0)$; see sketch (b) $y=0$ (c) $y=\pm\frac a2$ (d) $\frac{\sqrt3a^2}8$

2026 RI P1 Q8

2026 RI P1 Q8

Solution:

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