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Math Help - Find the Cos(2alpha) when its in the 2nd quadrant

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    Find the Cos(2alpha) when its in the 2nd quadrant

    Given and is in quadrant II, find exact values of the six trigonometric functions.

    = .

    = .

    = .
    = .

    = .

    = .

    I know I need to set cos(2\alpha)=1-2\sin^2(\alpha) which is then \frac{31}{49}=1-2\sin^2(\alpha) which is then 2\sin^2(\alpha)=1-\frac{31}{49} now I think I get 2\sin^2(\alpha)= \frac{49}{49}-\frac{39}{49}=\frac{18}{49} from here I need some help ? 2\sin^2(\alpha)=\frac{18}{49}
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    Re: Find the Cos(2alpha) when its in the 2nd quadrant

    something's wrong here ... if 2\alpha is in quad II , then \cos(2\alpha) < 0. Your posted value for \cos(2\alpha) > 0
    Thanks from topsquark
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    Re: Find the Cos(2alpha) when its in the 2nd quadrant

    Quote Originally Posted by skeeter View Post
    something's wrong here ... if 2\alpha is in quad II , then \cos(2\alpha) < 0. Your posted value for \cos(2\alpha) > 0
    I realized that but this is the online question I need to answer from the university, my \cos(2\alpha) should be a negative number if it is in the quad II
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    Re: Find the Cos(2alpha) when its in the 2nd quadrant

    Quote Originally Posted by M670 View Post
    Given and is in quadrant II, find exact values of the six trigonometric functions.

    There is a serious flaw with this question.

    If 2\alpha\in II then it is impossible that \cos(\2\alpha)=\frac{31}{49}.

    The \cos is negative in quadrant II.
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    Re: Find the Cos(2alpha) when its in the 2nd quadrant

    Is there anyway to solve this problem as it's due for Monday? If say I tried to solve for \cos(2\alpha)=-\frac{31}{49}
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    Re: Find the Cos(2alpha) when its in the 2nd quadrant

    Quote Originally Posted by M670 View Post
    I realized that but this is the online question I need to answer from the university, my \cos(2\alpha) should be a negative number if it is in the quad II
    ... then you need to contact the responsible someone at your university and let them know the error.
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    Re: Find the Cos(2alpha) when its in the 2nd quadrant

    See this is a bit of a problem I am at a university in Montreal that is using this program developed and maintained by the university of Rochester, so getting a response is very slow....
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    Re: Find the Cos(2alpha) when its in the 2nd quadrant

    your last step ...

    2\sin^2{\alpha} = \frac{18}{49}

    so ... \sin{\alpha} = \, ?
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    Re: Find the Cos(2alpha) when its in the 2nd quadrant

    Quote Originally Posted by skeeter View Post
    your last step ...

    2\sin^2{\alpha} = \frac{18}{49}

    so ... \sin{\alpha} = \, ?
    I believe it would be \sin{\alpha} = \frac{\frac{\sqrt18}{49}}{2}
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    Re: Find the Cos(2alpha) when its in the 2nd quadrant

    no.

    2\sin^2{\alpha} = \frac{18}{49}

    \sin^2{\alpha} = \frac{9}{49}

    \sin{\alpha} = \pm \frac{3}{7}

    now ... you have to determine which is the correct value (the plus or the minus value). how will you determine that?
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    Re: Find the Cos(2alpha) when its in the 2nd quadrant

    That would be determined by the fact the question is asking me to look in the 2nd quad and sin of an angle in QII is positive
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    Re: Find the Cos(2alpha) when its in the 2nd quadrant

    if ...

    \frac{\pi}{2} < 2\alpha < \pi

    then ...

    \frac{\pi}{4} < \alpha < \frac{\pi}{2}

    ... therefore, \alpha is an angle in quad I
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    Re: Find the Cos(2alpha) when its in the 2nd quadrant

    Quote Originally Posted by skeeter View Post
    something's wrong here ... if 2\alpha is in quad II , then \cos(2\alpha) < 0. Your posted value for \cos(2\alpha) > 0

    Don't you think it is pointless to continue to speculate on what the correct question should have been?

    I suspect that whoever wrote the question meant \alpha\in II. That would make all the information consistent and tell us 2\alpha\in IV.
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    Re: Find the Cos(2alpha) when its in the 2nd quadrant

    Well I just put inputted \sin(\alpha)=\frac{3}{7} and the answer is correct I received 17% out of 100 because I didn't answer the other 5 functions but I still have 1 more attempt to add in the rest of the answer correct..
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    Re: Find the Cos(2alpha) when its in the 2nd quadrant

    I believe \cos(\alpha)=\frac{x}{7} X=\sqrt40 so \cos(\alpha)=\frac{\sqrt40}{7} Does this make sense?
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