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

AI Thread Summary
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
 
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