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

Click For Summary
SUMMARY

The discussion centers on the notation of the tangent function, 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 lead to ambiguity regarding whether the function or its argument is being squared. The consensus is that while tan(x)^2 is syntactically acceptable, it lacks clarity compared to the more conventional notation tan^2(x). The inclusion of parentheses in tan(x)^2 is deemed necessary to avoid confusion.

PREREQUISITES
  • Understanding of trigonometric functions and their notation
  • Familiarity with mathematical syntax and conventions
  • Basic knowledge of function notation in mathematics
  • Experience with calculators that utilize trigonometric functions
NEXT STEPS
  • Research the differences between function notation and exponentiation in mathematics
  • Explore best practices for writing mathematical expressions clearly
  • Learn about the implications of notation in programming languages for mathematical functions
  • Investigate how different calculators interpret trigonometric function notation
USEFUL FOR

Mathematicians, educators, students, and anyone involved in teaching or learning trigonometry who seeks to clarify mathematical notation and avoid ambiguity in expressions.

xyz_1965
Messages
73
Reaction score
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?
 
Mathematics news on Phys.org
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
 

Similar threads

  • · Replies 28 ·
Replies
28
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
2
Views
1K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
Replies
8
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 11 ·
Replies
11
Views
3K
Replies
16
Views
2K
Replies
2
Views
2K