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Math Help - Giving answers to the nearest degree, find in the interval 0<x<360

  1. #1
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    Giving answers to the nearest degree, find in the interval 0<x<360

    Giving answers to the nearest degree, find in the interval 0<x<360 all the solutions of:

    10 sin(x+26) cos(x+26)=1

    rather than the answer, id like to know the solution ie how to work it out.

    i have my mock exam tomorrow, please answer me asap please.

    thanks,
    neilofbodom
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  2. #2
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    Re: Giving answers to the nearest degree, find in the interval 0<x<360

    Use the identity \displaystyle \sin{(2\theta)} \equiv 2\sin{(\theta)}\cos{(\theta)}. If you let \displaystyle x + 26 = \theta then

    \displaystyle 10\sin{(x + 26)}\cos{(x + 26)} \equiv 5\cdot 2\sin{(x + 26)}\cos{(x + 26)} \equiv 5 \sin{[2(x + 26)]}.

    So now you need to solve \displaystyle 5\sin{[2(x + 26)]} = 1.
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    Re: Giving answers to the nearest degree, find in the interval 0<x<360

    oh ok. so then, ill find what x is and use the general solution of sin to find the other values, right?
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    Re: Giving answers to the nearest degree, find in the interval 0<x<360

    Yes. Remember that the sine function is positive in the first and second quadrants.
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    Re: Giving answers to the nearest degree, find in the interval 0<x<360

    ok thank you so much!
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