# Trigonomtetic inverses true or false problem?

• January 22nd 2011, 12:43 PM
homeylova223
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?(Wondering)
• January 22nd 2011, 12:46 PM
dwsmith
Quote:

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?(Wondering)

$\arccos(\cos(x))=x\Rightarrow\cos(\arccos(\cos(x)) )=\cos(x)\Rightarrow\text{note} \ \cos(\arccos(y))=y$

$\Rightarrow\cos(x)=\cos(x)$
• January 22nd 2011, 01:42 PM
skeeter
Quote:

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?(Wondering)

$\displaystyle \arccos\left[\cos\left(\frac{3\pi}{2}\right)\right] \ne \frac{3\pi}{2}$