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Math Help - Help with double angle and half angle formulas

  1. #1
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    Help with double angle and half angle formulas

    If cos(t) = -sqrt.(21)/5, sin(t) = -2/5 tan(t) = 2sqrt.(21)/21
    then what are the values of:

    cos (2t)

    sin (t/2)

    tan (2t)
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  2. #2
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    Quote Originally Posted by NeedHelp18 View Post
    If cos(t) = -sqrt.(21)/5, sin(t) = -2/5 tan(t) = 2sqrt.(21)/21
    then what are the values of:

    cos (2t)

    sin (t/2)

    tan (2t)
    note that angle t is in quadrant III.

    use the given values, plug and chug in the following formulas ...

    \cos(2t) = 2\cos^2{t} - 1 = 1 - 2\sin^2{t}

    \sin\left(\frac{t}{2}\right) = \sqrt{\frac{1 - \cos{t}}{2}}

    \tan(2t) = \frac{2\tan{t}}{1 - \tan^2{t}}
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