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Math Help - easy angle thing

  1. #1
    Senior Member furor celtica's Avatar
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    easy angle thing

    ok so i have this list of questions like this one:
    find the least positive value of B for which sin(A-B)=cos(A+B)

    using translation, odd, periodic properties, etc.
    the problem is i totally forgot how to work these out! i know there is a simple method to work this out without staring continually at the sin and cos graphs, i just need a little reminder. thanks
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  2. #2
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    Quote Originally Posted by furor celtica View Post
    ok so i have this list of questions like this one:
    find the least positive value of B for which sin(A-B)=cos(A+B)

    using translation, odd, periodic properties, etc.
    the problem is i totally forgot how to work these out! i know there is a simple method to work this out without staring continually at the sin and cos graphs, i just need a little reminder. thanks
    Dear furor celtica,

    \sin(A-B)=\cos(A+B)

    \cos\left(\frac{\pi}{2}-(A-B)\right)=\cos(A+B)

    \frac{\pi}{2}-(A-B)=2n\pi\pm(A+B)\mbox{ where }n\in Z

    A=\frac{\pi}{4}-n\pi\mbox{ or }B=n\pi-\frac{\pi}{4}\mbox{ where }n\in Z

    Therefore the smallest positive value for B would be,

    n=1\Rightarrow{B=\pi-\dfrac{\pi}{4}=\dfrac{3\pi}{4}}

    Hope you understood.
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  3. #3
    Senior Member furor celtica's Avatar
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    umm i got most of it but at the level i'm at the n is not really appropriate, could you kinda simplify that?
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  4. #4
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    Quote Originally Posted by furor celtica View Post
    umm i got most of it but at the level i'm at the n is not really appropriate, could you kinda simplify that?
    Dear furor celtica,

    Do you mean that you do not understand how we got the n into the equation?
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