Question

Define the inverse secant function by restricting the domain of the secant function to the intervals (0, pi/2) and (pi/2, pi), and sketch the inverse function’s graph.

Answer 1

sec = 1/cos
note cos is 0 at pi/2 so sec is undefined there (infinite + or -)
in quadrant I cos is + so sec is +
but in quadrant II cos is - so sec is -

note cos always </= |1| so |sec| always >/= |1|

that should help with your graph