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Math Help - double angle problem

  1. #1
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    double angle problem

    It says the sinx= 14/15 and it is in quadrant 2
    what quadrant is the sin2x in?
    (NO CALCULATOR)i figured it out with a calc but i cant w/out a calc

    i really need help fast thnx
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by brianH View Post
    It says the sinx= 14/15 and it is in quadrant 2
    what quadrant is the sin2x in?
    (NO CALCULATOR)i figured it out with a calc but i cant w/out a calc

    i really need help fast thnx
    \sin(2x)=2\sin(x)\cos(x)=2\cdot \frac{14}{15}\cdot \frac{\sqrt{29}}{15}
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  3. #3
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    i got that and it was -28 \frac{\sqrt{29}}{225}
    but how do i fugure out what quad thats in
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by brianH View Post
    It says the sinx= 14/15 and it is in quadrant 2
    what quadrant is the sin2x in?
    (NO CALCULATOR)i figured it out with a calc but i cant w/out a calc

    i really need help fast thnx
    We will use the identity sin(2x)=2sinxcosx to help us. Since sinx=\frac{14}{15}, we can determine that cosx=\frac{-\sqrt{29}}{15} (since sine was defined in the 2nd quadrant). Plugging this into the identity, we have:

    sin(2x)=2{\left(\frac{14}{15}\right)}{\left(\frac{-\sqrt{29}}{15}\right)}=\frac{-28\sqrt{29}}{225}.

    I'm going to conclude that sin2x falls in the 4th quadrant, since sin\theta=\frac{opp}{adj}. Since the opposite is negative, it will reside either in the 3rd or 4th quadrants. Since the adjacent is positive, it will reside in the 1st or 4th quadrants. Thus, the value of sin2x=\frac{-28\sqrt{29}}{225} satisfies the conditions for it to be in the 4th quadrant.

    Hope this helped you out!
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  5. #5
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by TheEmptySet View Post
    \sin(2x)=2\sin(x)\cos(x)=2\cdot \frac{14}{15}\cdot \frac{\sqrt{29}}{15}
    I'm sure you're missing a negative for the cosine term. Sine is positive in the second quadrant, whereas cosine is negative!
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  6. #6
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    thnx, it was a question on a test that i have to finish tomorrow at school
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  7. #7
    Behold, the power of SARDINES!
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    Quote Originally Posted by Chris L T521 View Post
    I'm sure you're missing a negative for the cosine term. Sine is positive in the second quadrant, whereas cosine is negative!
    Thanks I remembered while I was washing some dishes that I forgot to check what quadrants it was in.

    Sorry
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  8. #8
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    hehe! I always forget the quadrant!
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