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Math Help - Half/Double angle Problem

  1. #1
    Member ~berserk's Avatar
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    Half/Double angle Problem

    Given that \sin u=\frac{7}{25} and \tan u<0
    Find the exact value of \cos u,<br />
\sin 2u,<br />
\cos 2u,<br />
\tan 2u,<br />

    I was absent this day in class and am not sure about where to start with this problem. I obviously know that you won't do them all, and I don't expect you to or else I'd never learn! But guidance on how to do find \cos u and possibly one of the double angle ones would be greatly appreciated.
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  2. #2
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    \sin(a+b) = \sin(a)\cos(b) + \cos(a)\sin(b)
    \cos(a+b) = \cos(a)\cos(b) - \sin(a)\sin(b)

    You can derive the double angle identities from these, use \sin(2u) = \sin(u+u).

    Also, to find \cos(u) to use in the formulas use the facts \sin^2(u) + \cos^2(u) = 1 and \frac{\sin(u)}{\cos(u)} = \tan(u) to determine the sign.
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  3. #3
    Member ~berserk's Avatar
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    Could you clarify how to do the double angle ones please? As for the cos u i got \displaystyle{\frac{24}{25}} this was by recognizing that sin is opposite/hypotenuse and then i put the numbers in a triangle and found the adjacent side using Pythagorean theorem and found the side to be 24 and cos is adjacent/hypotenuse so that's how i got that part.
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  4. #4
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    First, cosine could be positive or negative. Use the information for tangent to figure out its sign.

    Can you try to write the formula for the double angle from the information I have given you before? There should be enough information.
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