So while doing some basic trig problems, I had a problem with $2\sin(\pi/6)-1$. $2\sin(\pi/6)$ is exactly $1$, but somehow $2\sin(\pi/6)-1$ is $-1.11\times10^{-16}$. 

I had previously thought that $\sin(\pi/6)$ is defined to be exactly $0.5$, especially because the ratio of a $30$-$60$-$90$ triangle is exactly $1$-$\sqrt{3}$ - $2$.

So why does this happen? Is $\sin(\pi/6)$ not actually exactly 0.5?

[![enter image description here](https://i.stack.imgur.com/Jed3T.png)](https://i.stack.imgur.com/Jed3T.png)