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C2: Trigonometrical equations

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    Hi everyone, I’ve got a question 3 \tan x + 2 \cos x = 0 that I really don’t know what to do with! I’d be really grateful if someone could give me some pointers.

    So I thought it would be the \tan \theta = \frac {\sin \theta}{\cos \theta} identity that would be useful here. So I rearranged to
    3 \frac {\sin x}{\cos x}  + 2 \cos x = 0 but then after that my mind froze and I really didn’t know what to do! :confused:
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    Multiply each term by cos x. Now it is possible to form a quadratic equation in sin x.
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    (Original post by Mr M)
    Multiply each term by cos x. Now it is possible to form a quadratic equation in sin x.
    Applying knowledge of cos2x+sin2x=1, additionally.
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    you are going the right way. after where you got upto youget (3sinx/cosx)+2cosx=0 therefore (3sinx/cosx)=-2cosx so then 3sinx = -2cos^2x you should know what cos^2x is equivalent to and then when you substitute that you get a quadratic equation and get two values for sin x and then solve them for their given ranges. i dunno if im doing this right because you havent given the answer but i got sinx = -0.5 or 2
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    (Original post by dslc)
    Applying knowledge of cos2x+sin2x=1, additionally.
    I bet you blurt out the punchlines to jokes too.
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    (Original post by Mr M)
    I bet you blurt out the punchlines to jokes too.
    Well actually, what you said was wrong.

    It wasn't possible to form a quadratic without applying the information I added.

    Apologies if I stole a little of your TSR thunder though.
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    (Original post by dslc)
    Well actually, what you said was wrong.

    It wasn't possible to form a quadratic without applying the information I added.

    Apologies if I stole a little of your TSR thunder though.
    "The butler did it!"
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    Thanks everyone for your help - that's really cleared it up for me
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    (Original post by dslc)
    Applying knowledge of cos2x+sin2x=1, additionally.
    Could please help me with some statistic concepts?
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    (Original post by kingfisher)
    Could please help me with some statistic concepts?
    I can try and help you with some statistics concepts, yes.

    Perhaps consider starting a new thread however, given that they'd be unrelated to trigonometrical equations.

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Updated: April 13, 2012
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