1.4: Use compound-angle results to find an area

Using suitable results for $\displaystyle \mathrm{sin}\,(A+B)$ and $\displaystyle \mathrm{sin}\,(A-B)$,

(a) show that

Figure 4 shows a sketch of part of the curve with equation

(b) Use calculus to find the total area of the regions bounded by the curve and the $\displaystyle x$-axis between $\displaystyle x=0$ and $\displaystyle x=\frac{\pi}{2}$.

Give your answer to 3 significant figures.