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Math Help - Trigonemetric equation help

  1. #1
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    Trigonemetric equation help

    ??
    Last edited by astrostar; March 8th 2008 at 09:47 AM.
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  2. #2
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    Hello, astrostar

    You're almost there . . .


    1 -2\sin^2\!\theta + \cos^2\!\theta \:= \:0\;\text{ for }0^o \leq \theta < 360^o

    My answer so far:

    . . 1 + \sin^2\!\theta + \cos^2\!\theta \:= \:3\sin^2\!\theta

    . . 2 \:= \:3\sin^2\!\theta . . . . Good!

    We have: . 3\sin^2\!\theta \:=\: 2\quad\Rightarrow\quad \sin^2\!\theta \:=\:\frac{2}{3}\quad\Rightarrow\quad \sin\theta \:=\:\pm\sqrt{\frac{2}{3}}

    Therefore: . \theta \;\;=\;\;\sin^{-1}\left(\pm\sqrt{\frac{2}{3}}\right) \;\;\approx\;\; \left\{54.7^o,\:125.3^o,\:234.7^o,\:305.3^o\right\  }

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  3. #3
    GAMMA Mathematics
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    Quote Originally Posted by astrostar View Post
    Hi,

    Can you help me finish this equation off. The answer needs to be angles from 0 to 360degrees.

    1 - 2 sin^2 E + cos^2 E = 0

    My answer so far,

    1 + sin^2 E + cos^2 E = 3 sin^2 E

    2 = 3 sin^2 E

    Any help appreciated
    You were on the right track; just continue with what you were doing!

    2=3sin^2(E)

    sin^2(E)=\frac{2}{3}

    sin(E)=\pm \sqrt{\frac{2}{3}}

    E = sinh(\pm \frac{2}{3})

    You'll have to use your calculator for the last part!
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  4. #4
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    Thanks for your help
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