This is a question on my school summer studies paper in preparation for precalculus this year. My answer is 6.657 but the answer the teacher has given in the answer section is 2.352 and 3.931 with no explanation. I don't understand where I am going wrong. Using negative angle identities I know sec(-1.42) is same as sec(1.42). Then I enter into calculator, having first put in radians mode... 1/(cos 1.42) which gives me 6.657. What am I doing wrong ? or is the teachers answers wrong? I'm unable to liaise with the teacher over the summer vacation.
Can you show an image of the original problem? I think you (or someone else) copied it incorrectly.
Since the answer to sec(-1.42)
can't be in radians (it's just a ratio), I immediately suspected that it's really asking for the
inverse secant, not the secant. And in fact, when I find the inverse secant of -1.42 radians, it's 2.352... .
But then, if the answer is
not one value but two, then it must not be asking for the value of a function, but the
solution to an equation, which would be sec(x) = -1.42. The two solutions to that, in the interval [imath][0,2\pi)[/imath], are 2.352 and [imath]2\pi-\sec^{-1}(-1.42)\approx 3.931[/imath].
So, did you not show us what it actually said, or did the teacher write it wrong?
