We will first resolve the expression in the parenthesis
3/4pi can be converted to degrees:
since 1 pi = 180 degrees
3/4 pi = x degrees
[tex]\begin{gathered} x=\frac{3\pi\text{ x 180}}{4\text{ }\pi} \\ =135^0 \end{gathered}[/tex]sin (135) = 0.707 or
[tex]\sin \text{ 135 = }\frac{\sqrt[]{2}}{2}[/tex]We can then find
[tex]\begin{gathered} \sin ^{-1}(\frac{\sqrt[]{2}}{2}) \\ =\frac{3\pi}{4} \end{gathered}[/tex]So
[tex]\sin ^{-1}(\sin (\frac{3\pi}{4}))\text{ = }\frac{3\pi}{4}[/tex]
