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Math Help - A q about finiding a solution for a Trig. Function

  1. #1
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    A q about finiding a solution for a Trig. Function

    hi evreyone,
    here is the q:

    Find the solutions of the equation sin θ = 1/2 if:
    (a) θ is in the interval [0, 2 pi )
    (b) θ is any real number
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  2. #2
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    Quote Originally Posted by mHadad View Post
    hi evreyone,
    here is the q:

    Find the solutions of the equation sin θ = 1/2 if:
    (a) θ is in the interval [0, 2 pi )
    (b) θ is any real number
    The solutions exist in the first and second quadrand because you are trying to find positive one.

    The one in the first quadrand is \pi/6 then one in the second quadrand is, \pi-\pi/6=5\pi/6
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    i have read in a solution for a q that sin θ = 2 has no solution, why?
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  4. #4
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    Quote Originally Posted by mHadad View Post
    i have read in a solution for a q that sin θ = 2 has no solution, why?
    because -1<\sin\theta<1
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    Quote Originally Posted by Quick View Post
    because -1<\sin\theta<1
    Becuase,
    -1\leq \sin \theta \leq 1

    If you want to be cool you can write,
    |\sin \theta|<1
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  6. #6
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    Quote Originally Posted by ThePerfectHacker View Post
    Becuase,
    -1\leq \sin \theta \leq 1

    If you want to be cool you can write,
    |\sin \theta|<1
    |\sin \theta|\leq 1
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  7. #7
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    Quote Originally Posted by mHadad View Post
    hi evreyone,
    here is the q:

    Find the solutions of the equation sin θ = 1/2 if:
    (a) θ is in the interval [0, 2 pi )
    (b) θ is any real number
    If \theta is a solution of \sin(\theta)=1/2 then so is \theta_n = \theta+2\pi n, \ \ n=\pm 1, \ \pm 2, ....

    So using the solutions given by ImPerfectHacker we have:

    \pi/6+2 \pi n, n=0,\ \pm 1,\ \pm 2,\ ..., and 5 \pi/6+2 \pi n, n=0,\ \pm 1,\ \pm 2,\ ... comprise all the real solution.

    RonL
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  8. #8
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    Quote Originally Posted by Quick View Post
    |\sin \theta|\leq 1
    Wow, retard after a retard.
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