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Math Help - cos(x) * cos(x)

  1. #1
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    cos(x) * cos(x)

    Why is it that cos(x) * cos(x) = cos^2(x) as opposed to cos(x)^2 ?

    Is this something to do with the trig identities? What identities are useful to know off by heart?

    Thanks
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  2. #2
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    Re: cos(x) * cos(x)

    It's a convention and, as will all conventions, it eliminates ambiguity. Nothing to do with identities, they still hold.

    Is \cos(x)^2 equal to (\cos(x))^2 (a lot of brackets, especially if you have lots of trig functions) or \cos(x^2)?


    IMO there are only four trig identities you need to know

    \sin^2(x) + \cos^2(x) = 1

    \sin (A \pm B) = \sin(A)\cos(B) \pm \cos(A)\sin(B)

    \cos(A \pm B) = \cos(A)\cos(B) \mp \sin(A)\sin(B)

    \tan(x) = \dfrac{\sin(x)}{\cos(x)}

    You can derive all your other identities from these
    Last edited by Ackbeet; June 15th 2011 at 01:34 AM.
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  3. #3
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    Re: cos(x) * cos(x)

    Although it is not a good notation, many people don't write the ( ) in sin(x), just sin x. That would make it too easy to confuse (sin(x))^2 with sin(x^2). Of course, you can write (sin(x))^2 (with the parentheses) but it is simpler to write sin^2(x). In general, if f(x) is a function of x, f^2(x) means f(x)*f(x)= (f(x))^2.
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  4. #4
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    Re: cos(x) * cos(x)

    Quote Originally Posted by Consumariat View Post
    Why is it that cos(x) * cos(x) = cos^2(x) as opposed to cos(x)^2 ?
    FYI: Almost all computer algebra systems require it be written as \cos(x)^2.
    That took me for ever to do it that way.
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  5. #5
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    Re: cos(x) * cos(x)

    oooooooooo!!!!!!!!!!
    Thanks for that. I could never do cos^2 x on my calculator. Now i know how to do it
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  6. #6
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    Re: cos(x) * cos(x)

    Cheers for all the input. It's all a bit clearer now.

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