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Math Help - Need help solving a trig problem

  1. #1
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    Cool Need help solving a trig problem

    Solve each equation for all θ in radians
    sin θ = 1

    answer: π/2 +2Nπ

    π=Pie
    Last edited by RaphaelB30; February 5th 2009 at 03:50 PM. Reason: took out confusing sign
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  2. #2
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    For  \sin \theta = 1 there are an infinite number of solutions since the sine wave is continuous and is no restriction is set in the question. To find first you simply take the arcsin of 1:

     \theta = \arcsin 1
     \theta = 1.57...
    which is equivalent to  \frac {\Pi}{2}

    The above answer is the only time the sine wave has a y value of 1 for 0 \leq \theta \leq 2\Pi. However the question asks for all values of  \theta . For the rest of the solutions you add  \frac 2\Pi n
    Where n is any integer negative or positive. The 2 \Pi is used as the wave repeats every 2\Pi and the n covers the fact that is repeats n times in a positive and negative direction.

    Hope this helps you to understand it. If you need further explanation just ask.
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  3. #3
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    Quote Originally Posted by RaphaelB30 View Post
    Solve each equation for all θ in radians
    sin θ = 1

    answer: π/2 +2Nπ

    π=Pie
    you are expected to know that if \sin{\theta} = 1, then the primary value of \theta = \frac{\pi}{2} , and repeats for values of \frac{\pi}{2} + k \cdot 2\pi \, \, , \, \, k \in \mathbb{Z}.

    learn the unit circle ...






    btw, this is pi ...



    and this is pie ...

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  4. #4
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    Red face

    Skeeter,
    How did you know the primary value of the primary value of theta=pi/2.
    Last edited by RaphaelB30; February 5th 2009 at 05:20 PM. Reason: skeeter found way without calculator
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  5. #5
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    You might now arcsin as inverse sin?
    You can get this value by drawing the sine wave, it is also the sort of value you should memorise and not need a calculator for.

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  6. #6
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    Talking I understand.

    I understand now.
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