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Math Help - Solving trigonometric equatio

  1. #1
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    Lightbulb Solving trigonometric equatio

    Hello, could someone please help me. I couldnt work out these questions.

    I have to solve X within the domain 0 deg ≤ X ≤ 360 deg (X = pheta (degrees))

    1) tan X = -1
    2) sin X = -1/2
    3) cos X = 0
    4) cos X = -1/2

    Thank you.
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  2. #2
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    Re:

    You trigonometric inverses and then multiply by (180/pi)
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  3. #3
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    Quote Originally Posted by tom_asian View Post
    1) tan X = -1
    \tan x=-1\implies x=\arctan(-1)

    Does that make sense?

    Do the same with the others.
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  4. #4
    MHF Contributor red_dog's Avatar
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    These are fundamental trigonometric equations.
    \sin x=a\Rightarrow x=(-1)^k\arcsin a+k\pi,k\in\mathbf{Z}
    \cos x=b\Rightarrow x=\pm\arccos b+2k\pi,k\in\mathbf{Z}
    \tan x=c\Rightarrow x=\arctan c+k\pi,k\in\mathbf{Z}
    Then find the values of k for which 0\leq x\leq 2\pi and then multiply by \displaystyle\frac{180}{\pi}
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    by the way, it's "theta"


    did you get the questions done ok?
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  6. #6
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    Quote Originally Posted by Jhevon View Post
    by the way, it's "theta"


    did you get the questions done ok?
    I can do the questions now. thanks.. although i dont know what is "arc"
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  7. #7
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by tom_asian View Post
    I can do the questions now. thanks.. although i dont know what is "arc"
    "arc" as it is used here just means "inverse"

    so arctan(x) means the inversed tangent of x or as you may know it as \tan ^{-1}x
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  8. #8
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    Re:

    Re:
    Attached Thumbnails Attached Thumbnails Solving trigonometric equatio-46.gif  
    Last edited by qbkr21; August 26th 2007 at 12:24 AM.
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  9. #9
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    Quote Originally Posted by qbkr21 View Post
    Re::d
    ahh... thanks..

    so thats another way to call it. I just call it sin inverse, etc....
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  10. #10
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by tom_asian View Post
    ahh... thanks..

    so thats another way to call it. I just call it sin inverse, etc....
    yes
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