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

In summary, $\tan^2 (x)$ is the same as $(\tan x)^2$, while $\tan (x)^2$ is not proper notation as it is unclear whether the argument or the function is being squared. Some may use it as a shorthand for $\tan^2 (x)$, but it is not universally accepted.
  • #1
xyz_1965
76
0
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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  • #2
I don't consider \(\displaystyle \tan(x)^2\) to be proper notation. It is unclear whether the argument or the function is being squared.
 
  • #3
MarkFL said:
I don't consider \(\displaystyle \tan(x)^2\) to be proper notation. It is unclear whether the argument or the function is being squared.

I concur.
 
  • #4
$\tan(x)^2$ is an acceptable form of syntax for $\tan^2{x}$ used in many calculators.
 
  • #5
Personally I would like to see \(\displaystyle tan(x)^2 = tan(x) \cdot tan(x)\). My problem isn't with the 2 but with a -1. \(\displaystyle f^{-1}(x)\) may be equally considered to be \(\displaystyle \dfrac{1}{f(x)}\) or the inverse function of f(x).

So long as the parenthesis are included in \(\displaystyle tan(x)^2\) I have no problem with the expression.

-Dan
 

1. Is tan(x)^2 the same as tan^2(x)?

Yes, they are both proper notations for the trig function tangent squared. The ^2 simply indicates that the function is being squared.

2. Can I use tan^2(x) instead of tan(x)^2 in my calculations?

Yes, both notations are acceptable and will give the same result. However, it is important to be consistent with notation throughout your work.

3. Why is there a ^2 in the notation for tangent squared?

The ^2 indicates that the function is being squared, meaning it is being multiplied by itself. This is to distinguish it from the function tangent, which is written as tan(x) without the exponent.

4. Is tan(x)^2 the same as (tan(x))^2?

Yes, the parentheses do not change the meaning in this case. Both notations indicate that the function tangent is being squared.

5. Can I write tan^2(x) as tan(x^2) instead?

No, this would not be proper notation for tangent squared. The ^2 should always come after the function, not inside the parentheses.

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