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Math Help - Find the exact value of Cos 11.25 degrees

  1. #1
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    Find the exact value of Cos 11.25 degrees

    How do I find the exact value without any decimals?
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    Re: Find the exact value of Cos 11.25 degrees

    Quote Originally Posted by Eraser147 View Post
    How do I find the exact value without any decimals?

    Can you find an easy expression for \cos(4\theta)}~?.

    Because 45^o=4(11.25)^o.
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    Re: Find the exact value of Cos 11.25 degrees

    11.25 degrees = pi/16

    \cos 2\theta = 2 \cos^2 \theta - 1 \Rightarrow \cos \theta = \sqrt{\frac{1 + \cos 2\theta}{2}} (in the domain that we're interested in)

    Then just apply this half-angle formula a couple times to get your answer.
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    Re: Find the exact value of Cos 11.25 degrees

    So it would be Sqrt 1 + (2)11.25 divided by 2?
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    Re: Find the exact value of Cos 11.25 degrees

    Quote Originally Posted by Eraser147 View Post
    So it would be Sqrt 1 + (2)11.25 divided by 2?
    no ...

    \cos\left(\frac{x}{4}\right) = \sqrt{\frac{1 + \cos\left(\frac{x}{2}\right)}{2}} = \sqrt{\frac{1 + \sqrt{\frac{1+\cos{x}}{2}}}{2}}

    now let x = 45^\circ
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  6. #6
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    Re: Find the exact value of Cos 11.25 degrees

    ^ Makes a lot more sense. Thanks.
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