An Impossible Sign Pattern

Let $a > 0$, let $s_a$ be the minimum of $y = \sin x$ on $[a, 2a]$, and $t_a$ its minimum on $[2a, 3a]$. As $a$ varies, determine which of the following sign patterns cannot occur, with proof:

1. $s_a > 0$ and $t_a > 0$; 2. $s_a < 0$ and $t_a < 0$; 3. $s_a > 0$ and $t_a < 0$; 4. $s_a < 0$ and $t_a > 0$.