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# cos^2(a) or cos(a)^2

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Is there a difference between cos^2(a) or cos(a)^2 Thanks in advance, - wolf

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there most certainly is.

cos(a)^2 is taking the cosine of a squared

you wrote:

cos^2(a) which can be (cos(a))^2 which is cosine squared of a

To masonium:

no, they are not the same with the last sentence you wrote.

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I''d have to agree with masonium. So does Maple.

The notation used is ambiguous, but since it''s easy enough to put the "^2" inside the brakets, in practice the extra brackets are dropped when the entire cos() term is being squared.

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quote:
Original post by Geoff the Medio
I'd have to agree with masonium. So does Maple.

The notation used is ambiguous, but since it's easy enough to put the "^2" inside the brakets, in practice the extra brackets are dropped when the entire cos() term is being squared.

What if lets say a = 3x + 5 ?

Then:

cos (a)2 will be unequal to (cos a)2 quite blatantly.

In practice just like others the power will be between the trigonomtric function and the operand, but its kind of hard to do that here...unless I use html characters for it.

[edited by - nervo on September 25, 2003 3:12:43 AM]

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Interestingly enough, I graphed what I said above on my graphing calculator. I had to input cos((3x+5)^2) to be different from cos(3x+5)^2, which is the same as cos^2(3x+5).

So, I stand corrected. In practice though, I wouldn''t have written it that way.

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quote:
Original post by Nervo
cos (a)2 will be unequal to (cos a)2 quite blatantly.

In practice just like others the power will be between the trigonomtric function and the operand, but its kind of hard to do that here...unless I use html characters for it.

The function "cos(a)" is treated as whole notational unit (lack of better term?). It is not "cosine * a" such that "cos(a)^2" = "cos * a^2". Rather, it is "cos(a) ^ 2" = "(cos(a))^2".

At least, that''s how I think of it...

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quote:
Original post by Geoff the Medio
quote:
Original post by Nervo
cos (a)2 will be unequal to (cos a)2 quite blatantly.

In practice just like others the power will be between the trigonomtric function and the operand, but its kind of hard to do that here...unless I use html characters for it.

The function "cos(a)" is treated as whole notational unit (lack of better term?). It is not "cosine * a" such that "cos(a)^2" = "cos * a^2". Rather, it is "cos(a) ^ 2" = "(cos(a))^2".

At least, that''s how I think of it...

I understand. I believe that it comes down to one''s personal preference overall. For myself, I would avoid placing an exponent to the right so as to eliminate the possibility of mis-interpreting it in calculations. But for others this may not be a problem.

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just to say that I hate when my professors don''t enclose the variable inside the sin/cos.. functions with a couple of parenthesis, it''s so ambiguous.

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This is why the notation cos2a was adopted: it is unambiguous understood to be (cos a)2. It''s also very concise, and the lack of brackets means that complex expressions that use it are easier to understand.

So:
For (cos a) * (cos a) write cos2a.
For cos (a * a) write cos (a2).

Avoid cos a2 and cos (a)2 as they aren''t clear. Note that this it''s difficult to express this in code without extra brackets and/or temporary variables, complexity the mathematical notation avoids.

John

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