Explanation

(b) $y_{1} = 5\left\lbrack sin2\pi t + \sqrt{3}\ cos2\pi t \right\rbrack$
= $10\lbrack\frac{1}{2}\sin{2\pi t + \frac{\sqrt{3}}{2}\cos{2\pi t\ }\rbrack}\ $
= $10\lbrack\cos{\frac{\pi}{3}\sin{2\pi t + \sin{\frac{\pi}{3}\cos{2\pi t\rbrack}}}}\ $
= $10\lbrack(\sin{2\pi t + \frac{\pi}{3})\rbrack}\ $
$\Rightarrow \ \ A_{1} = 10$
Similarly, $y_{2} = 5\sin\left( 2\pi t + \frac{\pi}{4} \right)$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ A_{2} = 5$
Hence, $\frac{A_{1}}{A_{2}} = \frac{10}{5} = \frac{2}{1}$