How do you evaluate sin⁡(π6) ?

Explanation:
Start with an equilateral triangle of side 2. The interior angle at each vertex must be ${\displaystyle \frac{\pi }{3}}$ since 6 such angles make up a complete ${\displaystyle 2\pi }$ circle.
Then bisect the triangle through a vertex and the middle of the opposite side, dividing it into two right angled triangles.
These will have sides of length 2,1 and ${\displaystyle \sqrt{2^2-1^2}=\sqrt{3}}$. The interior angles of each right angled triangle are ${\displaystyle \frac{\pi }{3},\frac{\pi }{6}}$ and ${\displaystyle \frac{\pi }{2}}$ with the ${\displaystyle \frac{\pi }{6}}$ coming from the fact that we have bicested one of the ${\displaystyle \frac{\pi }{3}}$ angles.
Then:
${\displaystyle \sin \left(\frac{\pi }{6}\right)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{12}{}}$

The exact value of $\sin (\frac{\pi }{6})\text{is}\frac{1}{2}$
The result can be shown in multiple forms
Exact Form:$\frac{1}{2}$
Decimal Form:
0.5