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Thread: what is inverse sine of sin3 equal to?

  1. #1
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    what is inverse sine of sin3 equal to?

    Hi,

    $\displaystyle \sin^{-1}(sin3) $. Find the exact value.

    what is that equal to in exact value?

    it's not equal to 3 because the inverse sine function has a range of -pi/2 << y << pi/2.

    I graphed the inverse sine on mathematica and it gave me a value of 0.559 etc but I don't know how to find the exact value of this

    Thanks
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  2. #2
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    acctually in general in the equation $\displaystyle

    \sin^{-1}(sin3)
    $
    both the sin's will give no effect because finding sin3 and inversing it again with sin give 3 itself
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  3. #3
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    exact answer

    Let the expression be equal to x, x being angle.
    $\displaystyle
    sin^-1(sin(3))=x
    $
    $\displaystyle
    sin(x)=sin(3)
    $
    $\displaystyle
    x=3
    $
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  4. #4
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    Quote Originally Posted by differentiate View Post
    Hi,

    $\displaystyle \sin^{-1}(sin3) $. Find the exact value.

    what is that equal to in exact value?

    it's not equal to 3 because the inverse sine function has a range of -pi/2 << y << pi/2. ... correct

    I graphed the inverse sine on mathematica and it gave me a value of 0.559 etc but I don't know how to find the exact value of this

    Thanks
    note that an angle of measure 3 radians is in quad II.

    $\displaystyle \sin(3) = \sin(\pi-3)$ , where $\displaystyle \pi-3$ is a quad I angle

    $\displaystyle \arcsin[\sin(\pi-3)] = \pi-3$
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  5. #5
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    Quote Originally Posted by baqijan View Post
    Let the expression be equal to x, x being angle.
    $\displaystyle
    sin^-1(sin(3))=x
    $
    $\displaystyle
    sin(x)=sin(3)
    $
    $\displaystyle
    x=3
    $
    Go back and read the original post. 3 is not between $\displaystyle -\pi/2$ and $\displaystyle \pi/2$ $\displaystyle sin^{-1}(sin(x))= x$ is only true for x in that range.
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