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Math Help - arcsin(sin(x)) ?

  1. #1
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    arcsin(sin(x)) ?

    How do I know when arcsin(sin(x)) is

    x
    \pi - x or
    2\pi - x ?
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  2. #2
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    Quote Originally Posted by circuscircus View Post
    How do I know when arcsin(sin(x)) is

    x
    \pi - x or
    2\pi - x ?
    Set \alpha=\arcsin(\sin x)\implies\sin\alpha=\sin x
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  3. #3
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    The function \sin^{-1} (\sin x) is very interesting. But it gives back x when |x| \leq \frac{\pi}{2}.
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  4. #4
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    Yea but when it's like

    arcsin(sin(3))

    arcsin(sin(4))

    arcsin(sin(5))


    I think the first one is \pi-3, second one is \pi-4 but last one is \2pi-5 (I'm going by memory from the lecture but you get what I'm saying like when it is outside that |pi/2| bound, it gets weird but I'm going to get tested on that

    I don't understand why it is those values...
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  5. #5
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    Have a look at this picture.
    (I might find its Fourier series if I am bored. It looks nice).
    Attached Thumbnails Attached Thumbnails arcsin(sin(x)) ?-picture1.jpg  
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  6. #6
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    I'm sorry...I don't understand graphs too well...could you explain what it means? I think I understand like have the brief idea but I can't translate the stuff I see on the chart to like pi-3, 2pi-5, etc...
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  7. #7
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    Quote Originally Posted by circuscircus View Post
    I'm sorry...I don't understand graphs too well...could you explain what it means? I think I understand like have the brief idea but I can't translate the stuff I see on the chart to like pi-3, 2pi-5, etc...
    Let y=\sin^{-1} (\sin x). It means if you got at a certain point on the x-axis say x=\frac{\pi}{2} then the y-value is the output you get if you subsitute x for \frac{\pi}{2} in \sin^{-1}(\sin \frac{\pi}{2} ). The reason why I graphed it is so that you can just find all the values by just looking without calculating anything.
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