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Simple trig question

  1. May 5, 2014 #1
    Hi guys,

    This has caused me some confusion. Any help in this regard would be greatly appreciated.
    1. The problem statement, all variables and given/known data

    Given that [itex]\theta[/itex] is an acute angle with sin[itex]\theta[/itex]=19/51 find the exact value of cos[itex]\theta[/itex]

    2. Relevant equations

    3. The attempt at a solution

    All I seem to be getting based on my calculations are approximations. I have no idea how to actually obtain the exact value. Initially I took the inverse of sin[itex]\theta[/itex] to get [itex]\theta[/itex]=21.872....degree. Therefore the cos[itex]\theta[/itex]=0.928....I also tried using a right-angled triangle and finding the adjacent which I calculated to be 47.328... and dividing adj by hyp to see whether I get an exact value but got the same answer as before.

    Any help in this regard would be greatly appreciated.

    Thanks in advance.
  2. jcsd
  3. May 5, 2014 #2


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    What about ##\sin^2 + \cos^2 = 1##, exactly ? It means you get a square root in your answer, but it definitely is exact.
  4. May 5, 2014 #3
    :rofl: Genius.

    Thank you so much, I can't believe I didn't think of that.
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