Arcsec is a notation for the trigonometric function “arcsecant.” The function arcsec(z) takes an argument (denoted as “z”) and finds the angle magnitude. The argument for arcses is a “secant” function (abreviated as “sec”) value. If we consider a right triangle, the secant function is defined by the ratio of the hypotenuse length to the adjacent side length that is reverse to the cosine definition. Thus, cosine(angle)=1/ secant(angle).
Divide “1” by the argument “z” of the arcsec(z) function. Note, that “z” is equal to secant(angle) and 1/z is cosine (angle). For example, if arcsec(4) then cosine is “1/4” value or 0.25.
Using a calculator, calculate the arccosine (arccos) function of “1/z” to get arcsec(z). Angle=arcsec(z)= arccos(1/z). In the example, arcsec(4)= arccos(0.25)=75.52 degrees.
Calculate arcsecant if the function is given as arcsec(sec(Z)) e.g. arcsec(sec(45)). In such a case you do not need to calculate the secant value and then follow Steps 1 and 2. Instead, get an instant answer: arcsec equals Z. In this example, arcsecant of sec(45) is 45.