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Help with De Moivre question!!!!!!!

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  • 06-12-2008 6:27pm
    #1
    damienricefan
    Registered Users Posts: 165 ✭✭


    http://www.studentxpress.ie/papers/solnscomp07.pdf

    right look at b(i) in this link

    how does 15pie/4 become 1/root 2?????

    i looked in the tables and pie/4 is equal to 1/root 2 for cosine at 45 degrees

    does that mean any pie/4 will be 1/root 2 or - 1/root 2!!

    Help !!!


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    #2
    KnifeWRENCH
    Closed Accounts Posts: 11,148 ✭✭✭✭KnifeWRENCH


    damienricefan wrote: »

    does that mean any pie/4 will be 1/root 2 or - 1/root 2!!

    Help !!!

    No, it doesn't. Because Cos 2pi/4 = 0.

    pi radians is 180 degrees. So 15pi/4 radians is equal to (15 x 180)/4 = 675 degrees.

    You should know from the unit circle that Cos 45 = Cos (360 - 45)
    In the exact same way, Cos 45 = Cos (720 - 45), because 720 is just 360 times two.
    And 720 - 45 = 675

    i.e. Cos 675 = 1/root 2 and therefore Cos (15pi/4) radians = 1/root 2

    Is that explanation ok?


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    #3
    [Deleted User]
    Posts: 4,630 ✭✭✭ [Deleted User]


    Click

    See the way 315 degrees (360-315=45) has cosine of 1/rt2? Thats 7/4 times around the circle (going anti-clockwise), if you go around it another 8/4 times you'll get to the same point, 8/4 + 7/4 = 15/4. Thus it has the same cosine. I probably didn't explain that great but it might make some sense to you!

    Edit: The picture actually says rt2/2, but as you probably know thats the same as 1/rt2.


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    #4
    phasers
    Registered Users Posts: 18,159 ✭✭✭✭phasers


    Because my calculator says so


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    #5
    Davidius
    Registered Users Posts: 4,893 ✭✭✭Davidius


    15pi/4 radians = 15(180)/4 degrees = 675 degrees.

    A full circle is 360 degrees.
    cos(675) = cos(675-360) = cos(315)

    315 degrees is between 270 and 360 - The fourth quadrant

    In the fourth quadrant:

    cos A = cos (360-A)
    sin A = -sin(360-A)
    tan A = -tan(360-A)

    A = 315 degrees in this case.

    cos 315 = cos(360-315) = cos45 = 1/root2

    If you have something in the form zPi/4 it will usually turn out to be +/- 1/root2 but not always. Say if z = 2, 4, 6, 8 etc. or z = 1.223 or a number like that, you'll get a different answer.

    It should work for z = 1, 3, 5, 7, 9, 11, 13, 15, 17 etc.
    Naturally I haven't proven that.

    When in doubt, use a calculator. :pac:


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