Obtain a tangent-intercept triangle and qualify its endpoint

A curve has $x=\cos^2t$, $y=\sin^3t$, $0\le t\le\pi/2$.

(i) Sketch the curve.2 marks

(ii) The tangent at $(\cos^2\theta,\sin^3\theta)$ meets the x- and y-axes at $Q$ and $R$ respectively. With $O$ the origin, show that the area of triangle $OQR$ is $\tfrac1{12}\sin\theta(3\cos^2\theta+2\sin^2\theta)^2$. The source repeats the interval using $t$; the tangent parameter is $\theta$.6 marks