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Math Help - help me out

  1. #1
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    help me out

    If i know \sin x then how can we find \sin(\frac{x}{2})
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  2. #2
    Member SENTINEL4's Avatar
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    Maybe one way is that if you have sinx=y , where y is a number, find from the tables for which x you have y.
    Then if you find x, find x/2 and from the tables again find sin(x/2)
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  3. #3
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    If i know sin x = y from the trig table but i dont have sin (x/2), then????
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    If you know \sin{x} then you know x, if you know x you know \frac{x}{2} , if you know \frac{x}{2} then you know \sin{\frac{x}{2}}
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    Member SENTINEL4's Avatar
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    Quote Originally Posted by pomp View Post
    If you know \sin{x} then you know x, if you know x you know \frac{x}{2} , if you know \frac{x}{2} then you know \sin{\frac{x}{2}}

    Exactly
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  6. #6
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    ok....
    i know sin 45 = 1/sqrt 2
    but i dont know sin 22.5
    ?????
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  7. #7
    Member SENTINEL4's Avatar
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    By using trig tables you should be able to find it.
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  8. #8
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    Quote Originally Posted by SENTINEL4 View Post
    By using trig tables you should be able to find it.
    Is there 22.5 in a trig table ? -_-


    Note that since 45 is in the first quadrant, 45/2 is also in the first quadrant.

    We know that \sin x=2\cos\tfrac x2\sin\tfrac x2

    So \sin^2x=4\cos^2\tfrac x2\sin^2\tfrac x2

    Let T=\sin^2\tfrac x2

    Then \sin^2x=4(1-T)\cdot T=4T-4T^2

    This is a quadratic equation. In your situation, we have :

    4T^2-4T-\frac 12=0

    Solve for T, by remembering it's positive (because it's a square)
    And then take its square root, by remembering that it must be positive (because x/2 is in the first quadrant)
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  9. #9
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    Quote Originally Posted by jashansinghal View Post
    ok....
    i know sin 45 = 1/sqrt 2
    but i dont know sin 22.5
    ?????
    OK I understand what you are asking now, you want to express \sin{\frac{x}{2}} in some exact form, in terms of \sin{x} ? In that case you need to use the half angle formula:

    2 \sin^2{\frac{x}{2}} = 1 - \cos{x}
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