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Math Help - Trig help

  1. #1
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    Trig help

    If cos x + sin x =2/3, find the value of sin(2x)

    I've got that the solution is: -5/9, but how do you get this?
    Last edited by white_cap; November 15th 2007 at 05:54 PM.
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  2. #2
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    Hello, white_cap!

    If the answer is . \text{- }\frac{5}{9}, there must be typo . . .


    If \cos x + \sin x \:=\:\frac{2}{3}, .find the value of {\color{red}\sin}(2x)

    Square both sides: . (\cos x + \sin x)^2 \:=\:\left(\frac{2}{3}\right)^2\quad\Rightarrow\qu  ad \cos^2\!x + 2\cos x\sin x + \sin^2\!x \;=\;\frac{4}{9}

    And we have: . \underbrace{\sin^2\!x + \cos^2\!x}_{\text{This is 1}} + 2\sin x\cos x \;=\;\frac{4}{9}

    Then: . 1 + \underbrace{2\sin x\cos x}_{\text{This is }\sin(2x)} \:=\:\frac{4}{9}

    Therefore: . 1 + \sin(2x) \:=\:\frac{4}{9}\quad\Rightarrow\quad \sin(2x) \;=\;-\frac{5}{9}

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  3. #3
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    Thanks so much, you're right it should have read:

    if cosx + sinx = 2/3 find the value of sin2x

    sorry about that, and thanks for providing the awnser AND correcting my mistake
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