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Math Help - find x

  1. #1
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    find x

    hi i am stuck on a question ..pls can you help:

    tanx(squared) + 3tanx + 2 = 0

    find x:

    i got (tanx +1)(tanx+2) = 0

    tanx = -1, tanx = -2
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  2. #2
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    Re: find x

    Quote Originally Posted by janvi anish View Post
    tanx(squared) + 3tanx + 2 = 0
    find x:
    i got (tanx +1)(tanx+2) = 0
    tanx = -1, tanx = -2
    If the question is \tan^2(x) + 3\tan(x) + 2 = 0 then yes so far so good.
    But the you posted it, it reads \tan(x^2). Learn to post correctly.

    Now you can use the \arctan\text{ function }.
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  3. #3
    MHF Contributor ebaines's Avatar
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    Re: find x

    Looks good, so far. For the solution tan(x) = -1 you now need to determine the angle x where tan(x) = -1. Hint - it's where sin(x) = -cos(x), and could be in quadrant 2 or 4. For tan(x) = -2 it's little more complicated - again it's in quadrant 2 or 4, but you'll have to find the angle using arctangent(-2).
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  4. #4
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    Re: find x

    thanks
    what is arctan? is it tan-1 (like to find angles on the calcualtor or shift tan)
    i know that the answer is -45 and 136 because when you use -1 and tan-1 it, those are the answers but and put it into the original equation it equals 0 so it works but i dont understand how -2 works. when you tan-1 it, the answer is -63... and 117... so when you substitute that into the original equation it doesnt equal 0 so im not sure why -1 works and why -2 doesnt?
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  5. #5
    MHF Contributor ebaines's Avatar
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    Re: find x

    Yes, arctangent(x) is often written as  tan^{-1}x. You have the correct answers -- -45 and 115 degrees (not 136) are equal to arctan(-1), and -63.4 and 116.6 degrees equal arctan(-2). When you put these values into the original equation it should work (it does for me):

     tan^2(116.6) + 3 tan(116.6) + 2 = (-2)^2 +3(-2) + 2 = 0

     tan^2(-63.4) + 3 tan(-63.4) + 2 = (-2)^2 +3(-2) + 2 = 0
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  6. #6
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    Re: find x

    okay! thank you for your help!!!
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  7. #7
    MHF Contributor ebaines's Avatar
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    Re: find x

    Correction! I made a typo that I can't fix. This:

    Quote Originally Posted by ebaines View Post
    ... -45 and 115 degrees (not 136) ...
    should have been: -45 and 135 degrees.
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