$$\\f(x)=\frac{Log[1 + 3*Sin[x]^2]}{2}\\\\
f(\pi/2)=\frac{Log[1 + 3*Sin[\pi/2]^2]}{2}\\\\
$now is this meant to be $[sin(pi/2)]^2\;\;or\;\;\;sin[(pi/2)^2] \;\;??\\\\
$I will assume $\;\;[sin(pi/2)]^2\\\\
f(\pi/2)=\frac{Log[1 + 3*[sin(pi/2)]^2]}{2}\\\\
f(\pi/2)=\frac{Log[1 + 3*1]}{2}\\\\
f(\pi/2)=\frac{Log[2]}{2}\\\\
$ now you can do it on a calc$\\\\\\
f(0)=\frac{Log[1 + 3*[sin(0)]^2]]}{2}\\\\
f(0)=\frac{Log[1 + 0]}{2}\\\\
f(0)=0\\\\$$
$$\\f(x)=\frac{Log[1 + 3*Sin[x]^2]}{2}\\\\
f(\pi/2)=\frac{Log[1 + 3*Sin[\pi/2]^2]}{2}\\\\
$now is this meant to be $[sin(pi/2)]^2\;\;or\;\;\;sin[(pi/2)^2] \;\;??\\\\
$I will assume $\;\;[sin(pi/2)]^2\\\\
f(\pi/2)=\frac{Log[1 + 3*[sin(pi/2)]^2]}{2}\\\\
f(\pi/2)=\frac{Log[1 + 3*1]}{2}\\\\
f(\pi/2)=\frac{Log[2]}{2}\\\\
$ now you can do it on a calc$\\\\\\
f(0)=\frac{Log[1 + 3*[sin(0)]^2]]}{2}\\\\
f(0)=\frac{Log[1 + 0]}{2}\\\\
f(0)=0\\\\$$