Interpreting Expressions Involving Cosine SquaredDate: 03/16/2007 at 04:47:55 From: Mat Subject: What does cos^2 actually mean? I don't understand the difference between cos(x)^2, cos^2(x) and (cos (x))^2. Are they all same? I think I know what (cos(x))^2 is, and I think cos(x)^2 is not a valid term. It should probably be cos(x^2). So that leaves cos^2(x). I do not understand this term. Could you please explain it? Date: 03/16/2007 at 05:46:01 From: Doctor Peterson Subject: Re: What does cos^2 actually mean? Hi, Mat. Cos^2 is an old traditional notation that we still retain, though it is inconsistent with modern functional notation in some respects. It means the square of the cosine: cos^2(x) = (cos(x))^2 The expression is evaluated by finding the cosine of x and the squaring the result. To first square x and then find the cosine of the result, I don't think it's quite illegal to write cos(x)^2, but it would be sufficiently misleading that we avoid it. In particular, when you don't use the parentheses, cos x^2 means cos(x^2), not (cos x)^2. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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