# Homework Help: Restricting a cosine function

1. Nov 9, 2012

### EngnrMatt

1. The problem statement, all variables and given/known data

cosθ = 1.316581

2. Relevant equations

cos-1cosθ = θ // if and only if 0$\leqθ\leq1$

3. The attempt at a solution

This problem is actually the result of an attempt at a solution to solve an even larger problem (SAS triangle specifically). I need to know how to restrict the cosθ value in order to get θ. If it helps any, the original fraction was (49-196.457081)/-112

I know its gotta be simple. I just have a terrible professor for math :P

2. Nov 9, 2012

### rock.freak667

Well cosθ > 1 will yield no real solutions as -1≤cosθ≤1

Meaning that the maximum value of cosθ is 1 and the minimum value is -1.

3. Nov 9, 2012

### SammyS

Staff Emeritus
As rock.freak667 point out, cos(θ) can never be greater than 1, nor less than -1.

Perhaps θ = 1.316581 and you need to find cos(∂).

As for your statement: cos-1cosθ = θ // if and only if 0 ≤ θ ≤ 1 , that's incorrect.

The correct statement is
$\displaystyle \cos^{-1}(\cos(\theta))=\theta\ \ \text{ if and only if }\ \ 0\le\theta\le\pi\ .$​