Calculus of a Single Variable, Chapter 5, 5.6, Section 5.6, Problem 4

arcsin(0)
Let this expression be equal to y.
y =arcsin(0)
Re-writing this equation in terms of sine function, it becomes:
sin (y) = 0
Base on the Unit Circle Chart (see attached figure), sine is zero at angles 0 and pi . So the values of angle y are:
y = 0, pi
Now that the values of angle y are known, refer to the original equation again.
y=arcsin (0)
Take note that the range of arcsine function is -pi/2lt=y lt=pi/2 .
Between the 0 and pi, the value that belongs to this interval is 0 only. So the solution to the original equation is:
y=arcsin (0)
y=0

Therefore, arcsin(0)=0 .