In this question you may use the values in the table below.
| \(\theta\) radians | \(\sin\theta\) | \(\cos\theta\) | \(\tan\theta\) |
|---|---|---|---|
| \(\dfrac\pi6\) | \(\dfrac12\) | \(\dfrac{\sqrt3}2\) | \(\dfrac{\sqrt3}3\) |
| \(\dfrac\pi3\) | \(\dfrac{\sqrt3}2\) | \(\dfrac12\) | \(\sqrt3\) |
Variables \(x\) and \(y\) are related by the equation \(y=\sin5x\) where \(0\le x\le\dfrac\pi{10}\).
Use calculus to find the approximate change in \(x\) when \(y\) increases from \(\dfrac{\sqrt3}2\) by the small amount 0.01.[4]
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