How do you evaluate #sec^-1(sec((19pi)/10))#?

1 Answer
Oct 13, 2016

#sec^-1(sec((19pi)/10))=sec^-1(sec((pi)/10))=pi/10#

Explanation:

#sec^-1(sec((19pi)/10))#

Since the restriction for secant inverse is #[0,pi],y!=pi/2# we can see that #(19pi)/10# is in quadrant four which is out of the restriction but since secant is positive in quadrant IV we need to find the argument in quadrant I from our restriction. So the reference angle is #pi/10# and therefore the argument in quadrant I is also #pi/10#.

Applying the property #f^-1(f(x))=x# we have our answer is #pi/10#