0606 P13 - Nov 2025 - Q3 - 4 marks
7068
In this question you may use the values in the table below.
| \(\theta\) radians | \(\sin\theta\) | \(\cos\theta\) | \(\tan\theta\) |
|---|---|---|---|
| \(\frac{\pi}{6}\) | \(\frac12\) | \(\frac{\sqrt3}{2}\) | \(\frac{\sqrt3}{3}\) |
| \(\frac{\pi}{3}\) | \(\frac{\sqrt3}{2}\) | \(\frac12\) | \(\sqrt3\) |
Variables \(x\) and \(y\) are related by the equation \(y=\sin5x\), where \(0\leqslant x\leqslant\frac{\pi}{10}\).
Use calculus to find the approximate change in \(x\) when \(y\) increases from \(\frac{\sqrt3}{2}\) by the small amount \(0.01\).
