<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] $2\pi$ radians represents a full circle turn so 


*

*$\sin(2\pi+\theta)=\sin(\theta)$ and 

*$\sin(2\pi-\theta)=\sin(-\theta)=-\sin(\theta)$ 


So $\sin \left(\frac{19}{12}\pi\right) = \sin \left(2\pi -\frac{5}{12}\pi\right) = \sin \left(-\frac{5}{12}\pi\right) = -\sin \left(\frac{5}{12}\pi\right)$ 
which since $\frac{5}{12}\pi=\frac{1}{6}\pi+\frac{1}{4}\pi$  makes $\sin \left(\frac{5}{12}\pi\right) = \sin \left(\frac{\pi}{6}+\frac{\pi}{4}\right) =\sin \left(\frac{\pi}{6}\right) \cos \left(\frac{\pi}{4}\right) + \cos \left(\frac{\pi}{6}\right) \sin \left(\frac{\pi}{4}\right) =\frac12 \sqrt{\frac12}+\frac{\sqrt{3}}{2} \sqrt{\frac12}$ and so gives $\sin \left(\frac{19}{12}\pi\right) = -\frac14 (\sqrt 2 + \sqrt 6) \approx -0.9659$
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