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Math Help - direction angles

  1. #1
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    direction angles

    Vector f has a direction angle a= 45 (degrees) it is known that cos b is twive as large as cos y find angles b and y (a= alpha b=beta, y= gama)

    i want to know if i did this equation right

    i know that cosb = 2cosy

    and i have the formula cos a^2 + cos b^2 + cos y^2=1
    so i plug in cosb=2cosy in for cosb^2

    and i get : cos45^2 + 2cosy^2 + cosy^2 = 1

    then: .5+ 3cosy^2=1

    3cosy^2= .5
    y= 65.9 deg

    then plug it back in to original

    so: cos45^2+cosb^2+cos 65.9^2=1

    then you get cosb^2=.333
    cosb=sqrt(.333)
    b=Cos^-1(.333)
    b=54.74deg

    thanks for the help
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  2. #2
    MHF Contributor

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    Quote Originally Posted by valvan View Post
    Vector f has a direction angle a= 45 (degrees) it is known that cos b is twive as large as cos y find angles b and y (a= alpha b=beta, y= gama)
    ??? It would be nice to know what "b" and "y" have to do with vector f!

    i want to know if i did this equation right

    i know that cosb = 2cosy

    and i have the formula cos a^2 + cos b^2 + cos y^2=1
    So a, b, and y ( \alpha, \beta, and \gamma) are the direction angles, the angles vector f makes with the x, y, and z axes? It would have been nice if you had said that to begin with!
    (I see now that you titled this thread "direction angles" but I still think you should have been more explicit.)

    so i plug in cosb=2cosy in for cosb^2

    and i get : cos45^2 + 2cosy^2 + cosy^2 = 1
    But you didn't do what you just said! If cos b= 2 cos y then cos^2 b= (2 cos y)^2= 4 cos^2 y.

    then: .5+ 3cosy^2=1=
    No. .5+ 5cos^2 y= 1 (and be careful: Write either cos^2 y or (cos y)^2. "cosy^2" means cos(y^2).)

    3cosy^2= .5
    y= 65.9 deg
    5 cos^2 y= .5 so cos^2 y= .1.

    then plug it back in to original

    so: cos45^2+cosb^2+cos 65.9^2=1

    then you get cosb^2=.333
    cosb=sqrt(.333)
    b=Cos^-1(.333)
    b=54.74deg

    thanks for the help
    Last edited by HallsofIvy; January 11th 2010 at 04:37 AM.
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