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Math Help - Solving a relatively easy trig. equation...

  1. #1
    Junior Member jonnygill's Avatar
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    Solving a relatively easy trig. equation...

    Hi!

    The equation is...

    2cos^2\Theta=2+sin^2\Theta

    i'm trying to solve for theta, limiting domain from 0 to 360 degrees.

    After substituting 1-sin^2\Theta for cos^2\Theta and simplifying i ended up with...

    -3sin^2\Theta=0 OR sin\Theta=\sqrt0

    after applying arcsine i came up with an answer of 0 degrees. Now, my graphing calculator of course does not provide ALL possible answers. I noticed that 180 degrees is also an answer. I guess this is because of the theoretical -0 degrees that when squared would result in 0 too?

    Did i do this correctly?
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  2. #2
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    e^(i*pi)'s Avatar
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    edit: my algebra sucked

    2 - 2\sin^2 \theta = 2 + \sin^2 \theta \rightarrow 3\sin^2 \theta = 0

    0 doesn't have a sign so squaring won't make a difference and you can simply solve \sin \theta = 0
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  3. #3
    Junior Member jonnygill's Avatar
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    ok this makes sense. but, 180 degrees is also an answer. since sin(180)=0. So, there are two answers. One the calculator gives me. How do i arrive at the fact that 180 degrees is also an answer?
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  4. #4
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    e^(i*pi)'s Avatar
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    From the graph of sin(x)

    \sin x = 0 \right \text{  hence  } x = 0 + 180n \text{  where  } n \in \mathbb{Z}

    Hence 360 is a potential solution depending on your domain.


    See the wolfram graph of sin(x): http://www.wolframalpha.com/input/?i...+from+0+to+2pi
    Last edited by e^(i*pi); February 17th 2011 at 04:33 PM. Reason: n is an integer, not x
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  5. #5
    Junior Member jonnygill's Avatar
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    ok, i get it.

    thank you.
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  6. #6
    Junior Member jonnygill's Avatar
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    actually that wasn't entirely true. I understand that since the graph intersects the x-axis at 0 pi and pi that these are two possible solutions.

    what i don't understand is how i would arrive at 180 degrees or pi as also being a solution.
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  7. #7
    MHF Contributor
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    Think of the unit circle. As you move along the unit circle, at which angles does the vertical distance become 0?
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  8. #8
    Junior Member jonnygill's Avatar
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    ok. so sin function gives you the y-coordinate and cos function gives you the x-coordinate. and tan gives you a ratio of the two.

    all within the unit circle of course.

    that is, when you plug in degrees.**
    Last edited by jonnygill; February 17th 2011 at 08:36 PM. Reason: typo
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