Trig question help. Please explain. I think the answer is supposed to be -1 but how do you know that it cannot be the other choices?

Look at the secant graph here :

https://www.desmos.com/calculator/g2ulbffk6j

Note  that  the range  is   ( - inf, -1 ] U [ 1, inf )

So.....the secant's  range  always has an absolute value   ≥  1

Only the first answer  meets that criteria....so....you are correct  !!

We know that sec(x) is equal to cos(x) because it is the reciprocal of cosine.

So, choice d cannot be correct because cos(x) cannot be 0, because it would result in an undefined answer. 

We we know that cosine is adjacent/ hypotenuse. Of course, the reciprocal would be hypotenuse/adjacent. 

If if you look at choice b, c, and e, the numerators (hypotenuse) are all smaller than the denominator (adjacent side). This is not possible because the hypotenuse in a triangle cannot be less than one side. 

this is why choice A must be correct