Answer
By use the graph of $f(x) = sinx, -\frac{\pi}{2} \lt x \leq \frac{\pi}{2}$ to find the absolute and local maximum and minimum values of f.
The sketch of the graph of f'in the interval $[-\frac{\pi}{2}, \frac{\pi}{2}]$
is shown below:
Work Step by Step
From the graph, observe that the absolute minimum of f is,
$f(-\frac{\pi }{2})= -1$
And the absolute maximum of f is,
$f(\frac{\pi }{2})= 1$
