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Math Help - arcsin(sin x) = x

  1. #1
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    arcsin(sin x) = x

    For what values of x is arcsin(sin x) = x?
    This is for a calculus class. I'm kind of confused.
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  2. #2
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    Quote Originally Posted by Mush89 View Post
    For what values of x is arcsin(sin x) = x?
    This is for a calculus class. I'm kind of confused.
    I suggest that you plot both these functions:
    f(x)=\arcsin(\sin(x))~\&~g(x)=x.
    Where do the graphs agree. And why?
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  3. #3
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    Hello, Mush89!

    \text{For what values of }x\text{ is }\,\arcsin(\sin x) \,=\, x\,?

    Interesting question!

    Since \arcsin always returns the principal value,
    . . I would say: . x \in \left[\text{-}\frac{\pi}{2},\:\frac{\pi}{2}\right]


    For other angles, say, \frac{5\pi}{6},

    . . we have: . \sin\frac{5\pi}{6} = \frac{1}{2}

    . . then: . \arcsin(\frac{1}{2}) \,=\,\frac{\pi}{6}

    That is: . \arcsin(\sin\frac{5\pi}{6}) \:=\:\frac{\pi}{6}

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