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Use a differential to estimate sin 31°, starting from sin 30° = 1/2…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Use a differential to estimate $\sin 31^\circ$ , starting from $\sin 30^\circ = \tfrac{1}{2}$ . Remember that the change of $1^\circ$ must be written in radians. Then compare the estimate with the value from a calculator, $0.515038$ , and give the size of the error.

Need a reminder? The key ideaShow

$dy = f'(x)\,dx$ and $f(x + dx) \approx f(x) + f'(x)\,dx$ . The relative error is $\dfrac{dx}{x}$ , the percentage error is $\dfrac{dx}{x} \times 100\%$ , and for $y = x^n$ the relative error in $y$ is $n$ times that in $x$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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