# Thread: Trigonomtetic inverses true or false problem?

1. ## Trigonomtetic inverses true or false problem?

Determine if the statement is true or false if it is false provide a counter example.

arcos (cosx)= x for all values of x
I am not sure what exactly I am supposed to for example if I chose o the arc cos would be pi/2 and if I chose arc cos zero the angle would be pi/2. So would that mean this statement is true or is it false?

2. Originally Posted by homeylova223
Determine if the statement is true or false if it is false provide a counter example.

arcos (cosx)= x for all values of x
I am not sure what exactly I am supposed to for example if I chose o the arc cos would be pi/2 and if I chose arc cos zero the angle would be pi/2. So would that mean this statement is true or is it false?
$\displaystyle \arccos(\cos(x))=x\Rightarrow\cos(\arccos(\cos(x)) )=\cos(x)\Rightarrow\text{note} \ \cos(\arccos(y))=y$

$\displaystyle \Rightarrow\cos(x)=\cos(x)$

3. Originally Posted by homeylova223
Determine if the statement is true or false if it is false provide a counter example.

arcos (cosx)= x for all values of x
I am not sure what exactly I am supposed to for example if I chose o the arc cos would be pi/2 and if I chose arc cos zero the angle would be pi/2. So would that mean this statement is true or is it false?
$\displaystyle \displaystyle \arccos\left[\cos\left(\frac{3\pi}{2}\right)\right] \ne \frac{3\pi}{2}$