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Thread: Single Trig Functions

  1. #1
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    Single Trig Functions

    Write the following as a single trigonometric function

    $\displaystyle 1/2sin12xcos12x$

    1/2 is a half, and the x value is theta, i wasn't sure how to do it that way. The question i have is this supposed to be 12theta, or should it be 2theta. i'm not sure how to do this.

    Thanks
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  2. #2
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    Quote Originally Posted by nuckers View Post
    Write the following as a single trigonometric function

    $\displaystyle 1/2sin12xcos12x$

    1/2 is a half, and the x value is theta, i wasn't sure how to do it that way. The question i have is this supposed to be 12theta, or should it be 2theta. i'm not sure how to do this.

    Thanks
    You're expected to know and use $\displaystyle \sin(2A) = 2 \sin (A) \cos (A)$.
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  3. #3
    Senior Member apcalculus's Avatar
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    Let's assume it says 12x.

    If we set u=12x, the expression becomes

    $\displaystyle 1/2 sin u cos u$

    The sine of a double angle formula says:

    $\displaystyle 2 sin u cos u = sin (2u)$

    Can you apply it here?

    At the end, remember to write the expression in terms of the original variable x. Good luck!
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  4. #4
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    $\displaystyle \frac{1}{2}\sin 12x \cos 12x$

    $\displaystyle \frac{1}{4}\times 2\sin 12x \cos 12x$

    Now apply $\displaystyle 2\sin u \cos u = \sin 2u$
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