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Homework Help: Definition of Acute Angle

  1. Jun 9, 2010 #1
    1. The problem statement, all variables and given/known data

    Let u=3i+0j+k and v=i-2j+k have a common tail. Let [tex]\theta[/tex] be the acite angle

    between u and v. Calculus sin[tex]\theta[/tex]

    2. Relevant equations

    ll u x v ll = ll u ll ll v ll sin[tex]\theta[/tex]

    3. The attempt at a solution

    First of all, I solved the problem already. To save time, I will not show my work, but show

    the answer I computed:

    sin[tex]\theta[/tex] = [tex]\frac{\sqrt{44}}{\sqrt{10}\sqrt{6}}[/tex]

    Which is equivalent to my textbook's answer:

    sin[tex]\theta[/tex] = [tex]\sqrt{\frac{11}{15}}[/tex]

    Now my question is how do I transform the answer I computed to the textbook's answer? I

    am pretty sure that it has to do with the concept of acute angles. Can anyone please

    explain this to me? Thanks.
    Last edited: Jun 9, 2010
  2. jcsd
  3. Jun 9, 2010 #2


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    Homework Helper

    √a√b = √ab

    √a/√b = √(a/b)
  4. Jun 9, 2010 #3


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    Staff Emeritus
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    An acute angle is just one that is between 0 and [tex]\frac{\pi}{2}[/tex]. Draw a pair of lines forming a (smallish) angle. There are two angles really formed, the obvious small one between them, and the huge one that's about 300 degrees on the other side.
  5. Jun 9, 2010 #4
    Hmmm, I see. But, I still do not know how to convert an obtuse angle to an acute angle. So

    let's pretend that I have a an angle, say:

    cos[tex]\theta[/tex] = [tex]\frac{-10}{\sqrt{22}\sqrt{42}}[/tex].

    How do I go about converting this angle into an acute angle without using a calculator?
  6. Jun 9, 2010 #5


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    It has nothing to do with the concept of acute angles. It's just algebra. Use the rules rock.freak posted to simplify the expression.
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