Arcsec(sec 7pi/6) = 5pi/6? why?

Question

Can anyone explain to me why Arcsec(sec 7pi/6) = 5pi/6 and not just 7pi/6? (where pi = 180 in degrees or 3.14 in radians)

Answer 1

Sec = 1/cos

Remember that cos acts as a wave function with a local maximum at pi, and is thus equal at points that are equidistant from pi. 7pi/6 and 5pi/6 are both pi/6 from pi, and are thus equal.

If cos is equal at two points, then sec is equal at the same 2 points.

Answer 2

Thats a really good question... what class is that in, sorry, I'm only taking college algebra... I think thats a little above me. Good luck with it though.