A curve $C$ has parametric equations \[x = \sin 2\theta, \quad y = \cos^2 \theta \quad \text{for}\

Question

A curve $C$ has parametric equations $$x = \sin 2\theta, \quad y = \cos^2 \theta \quad \text{for}\hspace{0.5em} 0 \le \theta \le \pi.$$ Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ in terms of $\theta$, expressing your answer in a single trigonometric function.[3] Find the rate of decrease of the gradient of $C$ at $\theta = \frac{\pi}{12}$ if $\theta$ is increasing at a constant rate of $\frac{\pi}{10}\text{ rad/s}$. Leave your answer in an exact form.[3]

Accepted Answer

(a) $-\dfrac12\tan2\theta$ (b) Rate of decrease $\dfrac{2\pi}{15}\text{ s}^{-1}$

2026 TMJC WA2 Q3

2026 TMJC WA2 Q3

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