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Math Help - Need help on this tricky question

  1. #1
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    Need help on this tricky question

    Find the sum: Cos^2 (0) + Cos^2 (2) + Cos^2 (4) + Cos^2 (356) + Cos^2 (358) + Cos^2 (360)

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by JohnLord123 View Post
    Find the sum: Cos^2 (0) + Cos^2 (2) + Cos^2 (4) + Cos^2 (356) + Cos^2 (358) + Cos^2 (360)

    Thanks in advance.
    1. I assume that the argument of the trigonometric functions is in degree (?).

    2. You can simplify the given term a little bit:

    Since

    \cos^2(0^\circ) = \cos^2(360^\circ) = 1

    \cos^2(2^\circ) = \cos^2(358^\circ)

    \cos^2(4^\circ) = \cos^2(356^\circ)

    you'll get:
    \begin{array}{l}<br />
\cos^2 (0^\circ) + \cos^2 (2^\circ) + \cos^2 (4^\circ) + \cos^2 (356^\circ) + \cos^2 (358^\circ) + \cos^2 (360^\circ)=\\<br /> <br />
2 + 2\cos^2(2^\circ)+2\cos^2(4^\circ)\end{array}

    Since 2\cos^2(2^\circ) = \cos(4^\circ)+1 the term simplifies to:

    2+1+ \cos(4^\circ)+2\cos^2(4^\circ) = \boxed{3+ \cos(4^\circ)(1+2\cos(4^\circ))}
    Last edited by earboth; August 23rd 2010 at 12:32 PM. Reason: removed a typo
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