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Math Help - Finding exact values for trigonometric functions

  1. #1
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    Finding exact values for trigonometric functions

    Hello,

    I am given a righ-triangle, where the h = sqroot(17), a =1, and b = 4. I am suppose to find the exact value of the trigonometric sin 4x. So, I use the double angle formula, and what results is 2 sin 2x cos 2x. Then, I use the the double angle formulas again, and get
    2[(2 sin x cos x)(1 - sin^2 x)]. After inputing the ratios for the angles, provided from the dimensions of the right-triangle, I get 256/289 as my exact answer; yet, the true
    answer--according to the book--is 240/289. Does anyone see where I went wrong?
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  2. #2
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    Re: Finding exact values for trigonometric functions

    Hello, Bashyboy!

    I am given a righ-triangle, where: h = sqrt(17), a = 1, and b = 4.
    I am suppose to find the exact value of the trigonometric sin 4x.
    So, I use the double angle formula, and what results is 2 sin 2x cos 2x.
    Then, I use the the double angle formulas again,
    . . and get: 2(2 sin x cos x)(1 - sin^2 x) .Here!

    \cos2x \:=\:2\cos^2\!x\!-\!1\,\text{ or }\,1\!-\!2\sin^2x\,\text{ or }\,\cos^2\!x\!-\!\sin^2\!x

    You were probably thinking of: . \cos^2\!x \:=\:1-\sin^2\!x

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  3. #3
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    Re: Finding exact values for trigonometric functions

    Oh, blimey. Thank you very much!
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