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Math Help - Trig problem

  1. #1
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    Unhappy Trig problem

    Can anyone help with this problem? Give the exact value of each expression.

    sin(2tan^-1 12/15)
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  2. #2
    hpe
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    Quote Originally Posted by jp25111
    Can anyone help with this problem? Give the exact value of each expression.

    sin(2tan^-1 12/15)
    Let's write atan for tan^-1.

    Then
    sin(atan(p/q)) = p/sqrt(p^2+q^2)
    (draw a right triangle with legs p and q and hypotenuse sqrt(p^2+q^2), the question is what is the sine of the angle whose tangent is p/q )
    and
    cos(atan(p/q)) = q/sqrt(p^2+q^2)
    (same argument).

    Also, by the double angle formula for the sine,

    sin(2theta) = 2sin(theta)cos(theta).

    Thus sin(2atan(p/q)) = 2pq/(p^2+q^2).

    You can generalize this to cos(2atan(p/q)) or sin(3atan(p/q)) etc. and anticipate what other questions your teacher might come up with
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  3. #3
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    I see said the blind man. Thanks!
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