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Math Help - Trigonomtetic inverses true or false problem?

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    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?
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    Quote Originally Posted by homeylova223 View Post
    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?
    \arccos(\cos(x))=x\Rightarrow\cos(\arccos(\cos(x))  )=\cos(x)\Rightarrow\text{note} \ \cos(\arccos(y))=y

    \Rightarrow\cos(x)=\cos(x)
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    Quote Originally Posted by homeylova223 View Post
    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\left[\cos\left(\frac{3\pi}{2}\right)\right] \ne \frac{3\pi}{2}
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