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Math Help - Solving trig

  1. #1
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    Solving trig

    Need help on how solve the following equation for 0 <= x <= 2\pi:
    This is what i have done, but it is incorrect.

    sin(2x)=cos(x)
    \frac{sin(2x)}{cos(x)}=0
    tan2x=0which gets 0

    P.S
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  2. #2
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    Smile

    Quote Originally Posted by Paymemoney View Post
    Need help on how solve the following equation for 0 <= x <= 2\pi:
    This is what i have done, but it is incorrect.

    sin(2x)=cos(x)
    \frac{sin(2x)}{cos(x)}=0
    tan2x=0which gets 0

    P.S
    your second step is wrong and so what follows.
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  3. #3
    MHF Contributor
    Grandad's Avatar
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    South Coast of England
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    Hello Paymemoney
    Quote Originally Posted by Paymemoney View Post
    Need help on how solve the following equation for 0 <= x <= 2\pi:
    This is what i have done, but it is incorrect.

    sin(2x)=cos(x)
    \frac{sin(2x)}{cos(x)}=0
    tan2x=0which gets 0

    P.S
    Noting that \sin2x = 2\sin x \cos x, we get:
    2\sin x \cos x = \cos x
    You need to be a little careful now. Don't just divide both sides by \cos x, because it might be zero, and the first commandment of arithmetic is 'Thou shalt not divide by zero'. So you need to say:
    2\sin x \cos x = \cos x

    \Rightarrow \cos x = 0 or 2\sin x = 1
    Can you go on to complete this now?
    Spoiler:
    (I get the answers x = \frac{\pi}{6},x = \frac{\pi}{2},x = \frac{5\pi}{6},x = \frac{3\pi}{2}.)


    Grandad
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  4. #4
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    thanks i get how to do it now
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