Plz help me with AP Calculus ?

Question

9.let y=f(x)=sin(arctanx). then the range of f is what?

Answer 1

the range of arctan x is (-pi/2 , pi/2).  the sin of an angle between -pi/2 and pi/2 is between -1 and 1.  

so the range of f is (-1, 1) or -1 < y < 1.

you can verify this using a graphing calculator.