# Theta in converting sec to cos

1. Nov 5, 2011

### vanmaiden

1. The problem statement, all variables and given/known data
I saw in my calculus book that something along the lines of arcsec $\frac{4}{\sqrt{pi}}$ = x was converted to arccos $\frac{\sqrt{pi}}{4}$ = x. I understand that sec and cos are reciprocals, but I don't see why has to be flipped as well.

2. Relevant equations
cos (θ), sec (θ)

3. The attempt at a solution
I began to think of the graphs and such, but I just can't think of why this works. I don't normally mess with the inverse trig functions and was hoping someone could point out what I'm missing.

Thank you.

2. Nov 5, 2011

### Staff: Mentor

Let x = $sec^{-1}\frac{4}{\sqrt{\pi}}$
Then sec(x) = $\frac{4}{\sqrt{\pi}}$
So cos(x) = $\frac{\sqrt{\pi}}{4}$
Which means that x = cos-1$\frac{\sqrt{\pi}}{4}$

It should be understood that there are domain restrictions on x.