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Math Help - How does the range of the cos function change with exponents?

  1. #1
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    Question How does the range of the cos function change with exponents?

    For example, what is the range of f(x) = cos^3 x? ...cos^2 x?

    I understand the range of cosx and sinx but I'm not sure how to adjust for the exponents. I think there must be something simple that I'm just missing, so if someone could explain, that would be great.

    Thanks.
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  2. #2
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    Re: How does the range of the cos function change with exponents?

    \cos^n(x) = (\cos(x))^n for positive n.

    In essence this means you take the range of cos(x) and raise both sides to the exponent n. Be wary of even exponents and negative numbers
    Last edited by e^(i*pi); July 14th 2011 at 02:51 PM.
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  3. #3
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    Re: How does the range of the cos function change with exponents?

    Hint: The range will be different for even powers of cos vs the odd powers. Does this help?
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    Re: How does the range of the cos function change with exponents?

    Quote Originally Posted by dsr430 View Post
    For example, what is the range of f(x) = cos^3 x? ...cos^2 x?
    If -1\le A\le 1 then -1\le A^3\le 1~\&~0\le A^2\le 1.
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    Re: How does the range of the cos function change with exponents?

    So the range is [-1, 1] when the exponent is odd and [0, 1] when the exp is even?
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    Re: How does the range of the cos function change with exponents?

    Quote Originally Posted by dsr430 View Post
    So the range is [-1, 1] when the exponent is odd and [0, 1] when the exp is even?
    This is correct for positive integral exponents.
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