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Math Help - Please Help me

  1. #1
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    Please Help me

    So I was trying to solve this problem arcsin(sin(-3pi/5)

    and so far I got that the arcsin(sin) can't cancel because the -3pi/5 is out the range of pi/2<x<-pi/2

    So I looked for the reference angle...
    and I know that -3pi/5 will lay on QIII because is going clockwise.
    So I looked at the theta hat, and I see that theta hat is -2pi/5..

    Is this right... or do I have a mistake... please help. I kind it feel that I did something wrong.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Please Help me

    I would use the following:

    \sin(-x)=-\sin(x)

    \sin^{-1}(-x)=-\sin^{-1}(x)

    \sin(\pi-x)=\sin(x)

    to obtain:

    \sin^{-1}\left(\sin\left(-\frac{3\pi}{5} \right) \right)=-\sin^{-1}\left(\sin\left(\frac{2\pi}{5} \right) \right)=-\frac{2\pi}{5}
    Thanks from TrimHonduras
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  3. #3
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    Re: Please Help me

    Also keep in mind that arcsine does not just have to be -90 degrees - 90 degrees, but can also be other sets of domains
    Thanks from TrimHonduras
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  4. #4
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    Re: Please Help me

    thanks guys!
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