Explanation

(d) $Y = 3\sin{31\ 4t + 4\cos{31\ 4t}}$
$= r\cos\theta\sin{314t + r\sin\theta}\cos 314t$
$= r\sin{(314\ t + \theta)}$ …(i)
Where $r\cos{\theta = 3}$ and $r\sin\theta = 4$
$\therefore\ \ \ r^{2}\left( \cos^{2}\theta + \sin^{2}\theta \right) = 3^{2} + 4^{2} = 25$
or $r = 5$ cm