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Math Help - Stumped again

  1. #1
    Junior Member Freaky-Person's Avatar
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    Stumped again

    Didn't even make it past question one... I have all the formulas, but I never learned how they were made... So basically, I can't modify them.

    \sin 3x = \cos 3x

    It looks so simple!! I would love to be able to do this myself, but I don't know what to do with that 3!!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Freaky-Person View Post
    Didn't even make it past question one... I have all the formulas, but I never learned how they were made... So basically, I can't modify them.

    \sin 3x = \cos 3x

    It looks so simple!! I would love to be able to do this myself, but I don't know what to do with that 3!!
    \sin \theta = \cos \theta when \theta = \frac {\pi}{4} + k \pi for some constant k

    so if \sin 3x = \cos 3x it means that 3x = \frac {\pi}{4} + k \pi

    now continue
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  3. #3
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    Hello, Freaky-Person!

    It's easier than you think . . .


    \sin 3x \,= \,\cos 3x

    Divide both sides by \cos3x\!:\;\;\frac{\sin3x}{\cos3x} \:=\:1 \quad\Rightarrow\quad \tan3x \:=\:1

    . . Then: . 3x \;=\;\frac{\pi}{4} + \pi n

    Therefore: . x \;=\;\frac{\pi}{12} + \frac{\pi}{3}n

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  4. #4
    Junior Member Freaky-Person's Avatar
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    Quote Originally Posted by Soroban View Post
    Hello, Freaky-Person!

    It's easier than you think . . .



    Divide both sides by \cos3x\!:\;\;\frac{\sin3x}{\cos3x} \:=\:1 \quad\Rightarrow\quad \tan3x \:=\:1

    . . Then: . 3x \;=\;\frac{\pi}{4} + \pi n

    Therefore: . x \;=\;\frac{\pi}{12} + \frac{\pi}{3}n

    I understand the n, and the k in the previous post, are some constant, but what constant?

    What am I supposed to do with all that? Where did all that come from? T.T
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Freaky-Person View Post
    I understand the n, and the k in the previous post, are some constant, but what constant?

    What am I supposed to do with all that? Where did all that come from? T.T
    it works for any and all integers. it is just there to show that the answer repeats itself and infinite number of times. so it works if we add 1 pi, or 2 pi or 3pi or ....

    how you deal with the constants depends on the original question. if the question asked for 0 \leq x \leq 2 \pi, then you should only choose those integers that cause the solution to fall in that interval, and you are generally expected to list all solutions in this interval, since it is not usually too many.
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