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-   -   Cos(x)= -1/2 (https://www.askmehelpdesk.com/showthread.php?t=284606)

  • Nov 24, 2008, 09:44 AM
    jynx3943
    cos(x)= -1/2
    Supposedly there are four possible solutions. My professor provided a worksheet that says cos(2pi/3) and cos(4pi/3) both equal -1/2, and cos(pi/3) and cos(5pi/3) both equal 1/2. How would I go about finding the other two values that equal -1/2??
  • Nov 24, 2008, 09:52 AM
    galactus
    The trig functions have periods. That is, they repeat after so long.

    Cosine has period of

    That is, they it repeats every 2Pi.

    i.e. and so on

    Use this to find the values where it equals cos(x)=-1/2.



    Now, enter integer values in for C. 0,1,2,3,.

    Try C=0 and we get

    Which

    If C=1, we get



    And so on and so on.

    Note the difference between

    If you want the interval , simply use the formula I gave you and root them out.
  • Nov 24, 2008, 09:57 AM
    galactus

    Does that help a little more?

    I bet it does. All you have to do is plug in integer values of C to find what radian measure gives -1/2 for your cosine
  • Nov 24, 2008, 10:01 AM
    jynx3943

    Thank you. This is kind of helpful, but I am still pretty confused as to why there can only be 4 possible values... aren't there endless values?
  • Nov 24, 2008, 10:09 AM
    galactus
    That's because you only want those in a certain interval. Most likely from 0 to 2Pi

    The two in that interval are

    For 1/2. they are

    I am assuming 0 to 2Pi is the interval you are using. You must know that.

    Look at the graph of cos(x). That will help visualize it.
  • Nov 24, 2008, 12:12 PM
    jynx3943

    I really appreciate all of your help galactus. I will find out what is going on with the wording of the question and let you know.
  • Nov 24, 2008, 12:18 PM
    galactus

    I fI was of help, would you please click the 'rate this answer' button

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