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Math Help - compound/double angle formulas

  1. #1
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    compound/double angle formulas

    If x is an acute angle such that tan2x = -24/7, find sinx and cosx.

    help? thanks
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by checkmarks View Post
    If x is an acute angle such that tan2x = -24/7, find sinx and cosx.

    help? thanks
    draw a right-triangle with acute angle 2x and opposite side 24 and adjacent side 7. use Pythagoras' theorem to find the hypotenuse.

    then you will know that cos(2x) = (adjacent)/(hypotenuse)

    then use the fact that \cos 2x = 2 \cos^2 x - 1 = 1 - 2 \sin^2 x to find sin(x) and cos(x)


    or you could solve.

    tan(2x) = -24/7

    => sin(2x)/cos(2x) = -24/7

    => 7 sin(2x) = -24 cos(2x)

    and use the double angle formulas to change everything to sine and cosine and continue
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