arcsin(1/2) Evaluate the expression without using a calculator

arcsin(1/2)
Let this expression be equal to y.
y =arcsin(1/2)
Rewriting it in terms of sine function, the equation becomes:
sin(y) = 1/2
Base on the Unit Circle Chart (see attached figure), sine is 1/2 at anglespi/6 and (5pi)/6. So the values of angle y are:
y = pi/6, (5pi)/6
Then, refer to the original equation again.
y = arcsin (1/2)
Take note that the range of arcsine is -pi/2lt=ylt=pi/2 . So it is only pi/6 that belongs to this interval. Hence, the solution is
y=arcsin(1/2)
y=pi/6
 
Therefore, arcsin(1/2)=pi/6 .