I4.1 Consider the function $y=\sin x+\sqrt{3} \cos x$. Let $a$ be the maximum value of $y$. Find the value of $a$
$$
y=\sin x+\sqrt{3} \cos x=2\left(\sin x \cdot \frac{1}{2}+\cos x \cdot \frac{\sqrt{3}}{2}\right)=2\left(\sin x \cdot \cos 60^{\circ}+\cos x \cdot \sin 60^{\circ}\right)=2 \sin \left(x+60^{\circ}\right)
$$
$a=$ maximum value of $y=2$