Find the Exact Value sin(1/(2/(5pi)))

$\sin (\frac{1}{\frac{2}{5 π}})$

Multiply the numerator by the reciprocal of the denominator.

$\sin (1 \frac{5 π}{2})$

Multiply $\frac{5 π}{2}$ by $1$ .

$\sin (\frac{5 π}{2})$

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\sin (\frac{π}{2})$

The exact value of $\sin (\frac{π}{2})$ is $1$ .

$1$