= Solution
With $b=1$, nonnegativity of the <probability density function> at both $t$ and $-t$ requires
$$
\cos t\geq |a|t,\qquad 0<t\leq h=\pi/6.
$$
This is equivalent to $|a|\leq\inf_{0<t\leq h}\cos t/t$. The <derivative>
$$
\frac d{dt}\left(\frac{\cos t}{t}\right)=-\frac{t\sin t+\cos t}{t^2}<0
$$
shows that this infimum occurs at $t=h$. Therefore the necessary and sufficient restriction is
$$
\boxed{-\frac{3\sqrt3}{\pi}\leq a\leq\frac{3\sqrt3}{\pi}.}
$$
Sufficiency follows from the same decreasing-ratio argument at every interior <point>. The endpoint values of $a$ are allowed: the <probability density function> merely vanishes at one endpoint.
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