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Math Help - It cant get easier than this ...

  1. #1
    Junior Member
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    Unhappy It cant get easier than this ...

    Hello,

    A question says solve sin(x)=-sqrt(3)/2 with no definite domain

    Now I know how simple this is ..
    But in class the teacher started explaining some weird stuff I couldnt understand.

    Anyway, I know that I do : arcsin(-sqrt(3)/2)
    ill get x=-60

    now arent I supposed to do the following ? :
    <br />
180-(-60)= 240

    So the solutions are -60 +2(pi)n ; n= +/- 1 +/- 2 +/- 3 ....
    and 240 +2(pi)n ; n= +/- 1 +/- 2 +/- 3 ....

    Is the answer correct ? or am I doing something wrong :S

    My teacher presented positive answers (+60) and not -60..
    and in Wolfram Alpha, the answers are 120 and 60 ..

    Please explain why

    Thanks !!
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by ZaZu View Post
    Hello,

    A question says solve sin(x)=-sqrt(3)/2 with no definite domain

    Now I know how simple this is ..
    But in class the teacher started explaining some weird stuff I couldnt understand.

    Anyway, I know that I do : arcsin(-sqrt(3)/2)
    ill get x=-60

    now arent I supposed to do the following ? :
    <br />
180-(-60)= 240

    So the solutions are -60 +2(pi)n ; n= +/- 1 +/- 2 +/- 3 ....
    and 240 +2(pi)n ; n= +/- 1 +/- 2 +/- 3 ....

    Is the answer correct ? or am I doing something wrong :S

    My teacher presented positive answers (+60) and not -60..
    and in Wolfram Alpha, the answers are 120 and 60 ..

    Please explain why

    Thanks !!
    your answers and work are fine. it only depends on the domain. if no domain has been given then just provide a general solution like you have done above.
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  3. #3
    Junior Member
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    Thanks for replying.

    But the teacher says he wants the answers to be like his :S

    Why does he get positive values ?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by ZaZu View Post
    and in Wolfram Alpha, the answers are 120 and 60 ..
    Not for me they aren't

    CB
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  5. #5
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    UPDATE

    Ok so I found out that there are both "Solutions" and "Elementary Solutions" in Wolfram Alpha.

    So


    Elementary solutions : x = -pi/3 = -60

    But what are " Solutions" for ?

    x = 2/3 (3 pi n+2 pi) =240, n element Z

    x = 1/3 (6 pi n-pi) =-60, n element Z

    Well anyway I got the 2 solutions correct, which is -60 and 240 ..

    Dont know where I went wrong ..

    I guess problem is solved then Im correct


    Thankksss all for replying
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