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Math Help - trigonometry (2)

  1. #1
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    trigonometry (2)

    Show that \theta=\pi/10 satisfies the equation sin2\theta=cos3\theta (I know how to do this ). Express this equation in terms of sin \theta and cos \theta . (I can do this too ) .

    Show that 4sin^2\frac{\pi}{10}+2sin\frac{\pi}{10}-1=0
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  2. #2
    Moo
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    Quote Originally Posted by thereddevils View Post
    Show that \theta=\pi/10 satisfies the equation sin2\theta=cos3\theta (I know how to do this ). Express this equation in terms of sin \theta and cos \theta . (I can do this too ) .

    Show that 4sin^2\frac{\pi}{10}+2sin\frac{\pi}{10}-1=0
    Haha I've got this equation while trying to do your other question

    What did you get for \sin 2\theta=\cos 3\theta in terms of sin and cos ?

    Something like 2\cos\theta\sin\theta=4\cos^3\theta-3\cos\theta (1) isn't it ? (next time, it's better you write the result you got, so that we can check it )

    Now, let \theta=\frac{\pi}{10}, which is correct, since it satisfies the initial equation.

    \cos\theta\neq 0, so you can divide both sides of (1) by \cos\theta to get 2\sin \frac{\pi}{10}=4\cos^2\frac{\pi}{10}-3

    Then just use the well-known identity \cos^2 a+\sin^2 a=1 to transform \cos into \sin


    That's all folks !
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  3. #3
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    Quote Originally Posted by Moo View Post
    Haha I've got this equation while trying to do your other question

    What did you get for \sin 2\theta=\cos 3\theta in terms of sin and cos ?

    Something like 2\cos\theta\sin\theta=4\cos^3\theta-3\cos\theta (1) isn't it ? (next time, it's better you write the result you got, so that we can check it )

    Now, let \theta=\frac{\pi}{10}, which is correct, since it satisfies the initial equation.

    \cos\theta\neq 0, so you can divide both sides of (1) by \cos\theta to get 2\sin \frac{\pi}{10}=4\cos^2\frac{\pi}{10}-3

    Then just use the well-known identity \cos^2 a+\sin^2 a=1 to transform \cos into \sin


    That's all folks !

    Thanks thank thanks thanks Moo , you are just so nice .. Thanks again

    ok i think i understand dy
    Last edited by thereddevils; August 9th 2009 at 07:55 AM. Reason: figured out the why's !
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