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Math Help - Trig Functions (easy)

  1. #1
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    Exclamation Trig Functions (easy)

    Hello, I need help with this equation

    Solve  \cos (\Theta) = \sqrt{2}/2 0   \leq \Theta < 2   \pi

    And I'm told to Give exact answers. Use fractions, if necessary


    Whoops a little LaTex error, now fixed.
    Last edited by OVechkin8; November 27th 2009 at 10:00 PM.
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  2. #2
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    The range of 0 to 2pi means an entire circle...so can you figure out what angle in 360 degrees has cos = 2\sqrt{2}?

    Hint... cos = adjacent over hypotenuse, so at what angles on the unit circle is the adjacent angle 2 and the hypotenuse \sqrt{2}?
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  3. #3
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    There was a LaTex error that I had to fix, but with the new equation the angle is 45 degrees. So, would it be pi/4, 3pi/4, 5pi/4, and 7pi/4??
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    Quote Originally Posted by OVechkin8 View Post
    There was a LaTex error that I had to fix, but with the new equation the angle is 45 degrees. So, would it be pi/4, 3pi/4, 5pi/4, and 7pi/4??
    Regarding your answer, not quite... according to your equation, the cos of theta is positive, so it can't be in all 4 quadrants. Cosine is only positive in quadrants I and IV. However, the reference angle is 45 degrees (or pi/4) so you've got the right answers in there. It's pi/4 and 7pi/4.
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  5. #5
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    hm, ok I got it.
    Last edited by mr fantastic; November 29th 2009 at 12:53 AM. Reason: Moved question to another thread (@OP: It wouldn't hurt to Thank people before tagging more questions to a thread).
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  6. #6
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    Quote Originally Posted by OVechkin8 View Post
    Hello, I need help with this equation

    Solve  \cos (\Theta) = \sqrt{2}/2 0   \leq \Theta < 2   \pi

    And I'm told to Give exact answers. Use fractions, if necessary


    Whoops a little LaTex error, now fixed.
    nothing to "solve" here ... it's just knowledge of the unit circle.

    \cos{\theta} = \frac{\sqrt{2}}{2}

    \theta = \frac{\pi}{4} \, , \, \frac{7\pi}{4}

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