Question

Find the exact value sin pi/6

Answer 1

`\begin{gathered} exact\text{ value:} \\ \sin ((\pi)/(6)) \end{gathered}`

in order to find the value of sin pi/6, we start using an equilateral triangle, which has the same value for its 3 inner angles

then we divide the triangle in half including the angle at the top of the triangle and we obtain

then using the definition of sin we obtain, in which op is the opposite side and hy is the hypotenuse

`\sin \alpha=(op)/(hy)`

replace in the formula

`\begin{gathered} \sin ((\pi)/(6))=((a)/(2))/(a) \\ \sin ((\pi)/(6))=(1)/(2) \end{gathered}`