MHB Is tan(x)^2 proper notation for the trig function tangent squared?

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The discussion centers on the notation for the tangent function squared, specifically comparing tan^2(x) and tan(x)^2. Participants agree that tan^2(x) clearly indicates (tan x)^2, while tan(x)^2 can be ambiguous regarding whether the argument or the function is squared. Some express that tan(x)^2 is acceptable syntax, particularly in calculators, but prefer clearer expressions like tan(x) * tan(x). The inclusion of parentheses in tan(x)^2 helps clarify the expression's meaning. Overall, clarity in mathematical notation is emphasized as crucial for understanding.
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Is tan^2 (x) the same as tan(x)^2?

Note: I could have used any trig function.

I know that tan^2 (x) means (tan x)^2.
What does tan (x)^2 mean? Is it proper notation?
 
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I don't consider $$\tan(x)^2$$ to be proper notation. It is unclear whether the argument or the function is being squared.
 
MarkFL said:
I don't consider $$\tan(x)^2$$ to be proper notation. It is unclear whether the argument or the function is being squared.

I concur.
 
$\tan(x)^2$ is an acceptable form of syntax for $\tan^2{x}$ used in many calculators.
 
Personally I would like to see [math]tan(x)^2 = tan(x) \cdot tan(x)[/math]. My problem isn't with the 2 but with a -1. [math]f^{-1}(x)[/math] may be equally considered to be [math]\dfrac{1}{f(x)}[/math] or the inverse function of f(x).

So long as the parenthesis are included in [math]tan(x)^2[/math] I have no problem with the expression.

-Dan
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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