<s>[INST] How do I reduce radian fractions? For example, I need to know $\sin (19π/12)$. 
I need to use the subtraction formula. How do I get $(\text{what}) - (\text{what}) = 19π/12$? I am stuck at what are the radians
Do I divde it by something? What is the process? 
 [/INST] $$\frac{19\pi}{12}=\pi+\frac{3\pi}4-\frac{\pi}6$$
Since $\sin(\pi+x)=-\sin x$, $\sin\left(\frac{19\pi}{12}\right)=-\sin\left(\frac{3\pi}4-\frac{\pi}6\right)$.
And since $\sin(A-B)=\sin A\cos B-\cos A\sin B$:
$$\begin{align}
-\sin\left(\frac{3\pi}4-\frac{\pi}6\right)&=-\left(\sin\left(\frac{3\pi}4\right)\cos\left(\frac{\pi}6\right)-\cos\left(\frac{3\pi}4\right)\sin\left(\frac{\pi}6\right)\right) \\
&=-\left(\frac{\sqrt{2}}2*\frac{\sqrt{3}}2-\left(-\frac{\sqrt{2}}2 * \frac12\right)\right) \\
&=-\frac{\sqrt{2}+\sqrt{6}}4
\end{align}$$
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