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How to find the exact value of cos 67.5 ?

  1. Feb 19, 2012 #1
    One of the questions in the homework for online precalc class I'm taking is to find the exact value for cos (67.5).
    At first I didn't realize that I should just take the half angle of 135, so instead I tried to find the value for cos (45 + 45/2), and got stuck at this point.

    attachment.php?attachmentid=44118&stc=1&d=1329679233.png

    If I calculate the actual value I get the correct answer, but I'm not able to see how I can simplify this further.
    I know the solution is as simple as finding the half angle value of

    attachment.php?attachmentid=44119&stc=1&d=1329679233.png

    Any suggestions of how I can get from my first attempt solution to the simpler (and correct) solution?
     

    Attached Files:

  2. jcsd
  3. Feb 19, 2012 #2
    How is Cos(x) related to Cos(x+90), how is Cos(x+90) related to other trig functions?
     
  4. Feb 19, 2012 #3

    vela

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    Try multiplying both the top and bottom by ##\sqrt{2-\sqrt{2}}##.
     
  5. Feb 19, 2012 #4
    >>How is Cos(x) related to Cos(x+90), how
    yeah, that definitely makes it simpler

    attachment.php?attachmentid=44137&stc=1&d=1329699522.png

    >>Try multiplying both the top and bottom by
    I have tried, but I seem to end up with a square root I can't get rid of, but I will keep trying.


    Thanks for your help
    Jesper
     

    Attached Files:

  6. Feb 19, 2012 #5

    ehild

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    Hi, jkristia,

    Square your formula for cos(45+45/2), simplify, and then take the square root.


    ehild
     
  7. Feb 20, 2012 #6
    ah - of course, that works
    Thank you very much
     
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