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Math Help - Solving Using Trig Idenities

  1. #1
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    Solving Using Trig Idenities

    I actually dunno what the identities for \cot^2 are...

    but anyway, your help is greatly appreciated.

    When  0\le x < 2\pi,
    solve 2 \cot^2 x + 3\csc x = 0

    Thanks!
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  2. #2
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    Quote Originally Posted by Savior_Self View Post
    I actually dunno what the identities for \cot^2 are...

    but anyway, your help is greatly appreciated.

    When  0\le x < 2\pi,
    solve 2 \cot^2 x + 3\csc x = 0

    Thanks!
    hi

     <br />
1+\cot^2 x=\csc^2 x<br />
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  3. #3
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    Hello Savior_Self
    Quote Originally Posted by Savior_Self View Post
    I actually dunno what the identities for \cot^2 are...
    There are three identities like this, and they all start with Pythagoras' Theorem:
    \text O^2+\text A^2 = \text H^2
    Divide both sides by \text H^2:
    \sin^2\theta + \cos^2\theta = 1 (Do you see? \sin^2\theta = \frac{\text O^2}{\text H^2} ... etc)
    Instead, divide by \text A^2:
    \tan^2\theta+1 = \sec^2\theta
    Now divide by \text O^2:
    1+\cot^2\theta  = \csc^2\theta
    Perhaps that will help you remember them!

    Grandad
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  4. #4
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    Quote Originally Posted by Grandad View Post
    Hello Savior_SelfThere are three identities like this, and they all start with Pythagoras' Theorem:
    \text O^2+\text A^2 = \text H^2
    Divide both sides by \text H^2:
    \sin^2\theta + \cos^2\theta = 1 (Do you see? \sin^2\theta = \frac{\text O^2}{\text H^2} ... etc)
    Instead, divide by \text A^2:
    \tan^2\theta+1 = \sec^2\theta
    Now divide by \text O^2:
    1+\cot^2\theta  = \csc^2\theta
    Perhaps that will help you remember them!

    Grandad
    Now that's just awesome.

    I've never seen it explained like that before. Thanks, Grandad! I'll remember that the rest of my life.
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