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Math Help - More double angle and Half angle problems

  1. #1
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    More double angle and Half angle problems

    tanx = -5/12; x in quad IV

    so I got tan 2x = -120/119 but I don't understand how to get sin2x and cos2x.

    cosx = 5/9; x in quad I

    Like the previous problem, I am able to get cos2x, which is -31/81, but I don;t know how to get the other 2 functions.

    Lastly,
    sinx = 2sin x/2 cos x/2
    I'm not really sure hot to prove this. It looks like a double angle sin identity.
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by hellojellojw View Post
    tanx = -5/12; x in quad IV

    so I got tan 2x = -120/119 but I don't understand how to get sin2x and cos2x.

    cosx = 5/9; x in quad I

    Like the previous problem, I am able to get cos2x, which is -31/81, but I don;t know how to get the other 2 functions.

    Lastly,
    sinx = 2sin x/2 cos x/2
    I'm not really sure hot to prove this. It looks like a double angle sin identity.
    \tan{x}=\frac{\sin{x}}{\cos{x}}...
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  3. #3
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    Quote Originally Posted by VonNemo19 View Post
    \tan{x}=\frac{\sin{x}}{\cos{x}}...
    Well, I'm not that dumb. I did try that, but I got the wrong answer.
    Unless I'm doing it wrong. Given tanx = -5/12 sinx = -5 cosx = 12
    Right????
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by hellojellojw View Post
    Well, I'm not that dumb. I did try that, but I got the wrong answer.
    Unless I'm doing it wrong. Given tanx = -5/12 sinx = -5 cosx = 12
    Right????
    Not quite... I never said you were dumb.

    -1\leq\sin{x}\leq1

    Same goes for cosine.

    Use the pythagorean theorem to find the hypotenuse (h) (where -5 and 12 are the legs, respectively). then \sin{x}=\frac{-5}{h}
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  5. #5
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    Quote Originally Posted by VonNemo19 View Post
    Not quite... I never said you were dumb.

    -1\leq\sin{x}\leq1

    Same goes for cosine.

    Use the pythagorean theorem to find the hypotenuse (h). then \sin{x}=\frac{-5}{h}
    ahahaha I guess I am dumb. so sinx = -5/13. Unless I'm still doing it wrong.
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  6. #6
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by hellojellojw View Post
    so sinx = -5/13.
    Indeed!
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