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    chanel18's Avatar
    chanel18 Posts: 1, Reputation: 1
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    #1

    May 31, 2010, 02:47 PM
    help with cos(180 degrees-x)=-cosx
    please help with verifying the identity: cos(180 degrees-x)=-cosx
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #2

    Jun 1, 2010, 06:01 AM

    Two ways to do this:

    1. Use the formula for the cosine of the sum of angles:

    cos(a+b) = cos(a)cos(b)-sin(a)sin(b),

    where a = 180 degrees and b = -x. Remember that sin(180)=0 and cos(180) = -1.

    2. Use some of the rues for graphing functions which you learned in algebra. First, consider the function cos(-x); because the cosine function is symmetric about the y axis the graph of cos(-x) is the same as cos(x). Next, consider that f(180-x) is equivalent to shifting the graph of f(x) to the left by 180. Put these two facts together and you see that the graph of cos(180-x) is the cos(x) graph shifted by 180. This put it exactly "out of phase" with cos(x), and hence cos(180-x) = -cos(x).

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