Question

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

Answer 1

`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`