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Math Help - cosine equation

  1. #1
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    cosine equation

    Right, im confused by this question...

    Find all the roots in the range -2π < x < 2π of the equation cos(2x) = 0.5 giving all the answers in radians as multiples of π.

    At first i thought it would be a (varying) cosine wave but how does that make sense, where is the 'y'? I thought by 'find the roots' it meant finding the angles at which the wave goes through the x axis between that range...

    any help. please? this is the last question and its in for tomorra
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by jugglingpirate View Post
    Right, im confused by this question...

    Find all the roots in the range -2π < x < 2π of the equation cos(2x) = 0.5 giving all the answers in radians as multiples of π.

    At first i thought it would be a (varying) cosine wave but how does that make sense, where is the 'y'? I thought by 'find the roots' it meant finding the angles at which the wave goes through the x axis between that range...

    any help. please? this is the last question and its in for tomorra
     <br />
\cos(y)=0.5 \Rightarrow y=\pm\pi/3+2n\pi,\ n=0,\pm1,\pm2,...<br />

    so if 2x=y, the roots are: x=\pm\pi/6+n\pi,\ n=0,\pm 1,\pm 2,....

    Now find the values of n which leave x in the required range.

    CB
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