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Math Help - Expressing Sin(2p) in terms of x

  1. #1
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    Expressing Sin(2p) in terms of x

    Hi,

    If x = 2sin(p)

    How do we express sin(2p) in terms of x only?

    Thanks
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  2. #2
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    Quote Originally Posted by algorithm View Post
    Hi,

    If x = 2sin(p)

    How do we express sin(2p) in terms of x only?

    Thanks
    sin (2p) = 2 sin p cos p.

    sin p = x/2. Use the Pythagorean Identity to get cos p from sin p = x/2.
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  3. #3
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    Quote Originally Posted by algorithm View Post
    Hi,

    If x = 2sin(p)

    How do we express sin(2p) in terms of x only?

    Thanks
    x = 2sin(p)
    sin (2p) = 2sin(p)cos(p)

    sin(2p) = x * cos(p)
    x = [sin(2p) / cos(p)]
    ----------

    (sorry mr. fantastic, didn't see you already explained it to him)
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  5. #5
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    Quote Originally Posted by algorithm View Post
    Hi,

    If x = 2sin(p)

    How do we express sin(2p) in terms of x only?

    Thanks
    hey mate,

    x = 2sin(p) --> sin(p) = x/2

    Trig Identity,

    sin(2p) = 2sin(p)cos(p) = 2 (x/2) cos(p) = xcos(p)

    note cos(p) = sqrt(1-sin^2(p)) = sqrt( 1 - (x/2)^2 ) = sqrt(1 - x^2/4) = sqrt( (4 - x^2)/4)
    = sqrt(4-x^2)/2

    Hence,

    sin(2p) = xcos(p) = x (sqrt(4-x^2)/2) = (x/2)sqrt(4-x^2)

    Hope this helps,

    David
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