Difference between arctan(x) and cot(x)

  • Thread starter Thread starter paridiso
  • Start date Start date
  • Tags Tags
    Difference
Click For Summary
SUMMARY

The discussion clarifies the distinction between the functions arctan(x) and cot(x). Arctan(x), defined as tan-1(x), is the inverse function of tan(x), while cot(x) is defined as 1/tan(x). The confusion arises from the notation, where arctan(x) does not equate to cot(x) due to their differing mathematical definitions and properties. Understanding these differences is crucial for accurate function application in trigonometry.

PREREQUISITES
  • Understanding of trigonometric functions, specifically sine, cosine, and tangent.
  • Familiarity with inverse functions and their notation.
  • Basic knowledge of function restrictions to maintain their one-to-one nature.
  • Ability to manipulate and interpret mathematical expressions involving trigonometric identities.
NEXT STEPS
  • Study the properties of inverse trigonometric functions, focusing on arctan and its domain and range.
  • Learn about the cotangent function and its relationship with tangent in various contexts.
  • Explore the graphical representations of arctan(x) and cot(x) to visualize their differences.
  • Investigate the implications of function notation in mathematics to avoid common misconceptions.
USEFUL FOR

Students of mathematics, educators teaching trigonometry, and anyone seeking to deepen their understanding of trigonometric functions and their inverses.

paridiso
Messages
17
Reaction score
0
If arctan(x) = tan(x)^-1 and since tan(x) = sin(x)/cos(x) is not arctan(x) = cot(x). I know something's not right here but what is it?

Thanks.
 
Physics news on Phys.org
No no.
Cot(x)=1/tan(x)

arctan(x)=tan-1(x) \neq1/tan(x)
 
rock.freak667 said:
No no.
Cot(x)=1/tan(x)

arctan(x)=tan-1(x) \neq1/tan(x)

Just to clarify, that notation doesn't mean the multiplicative inverse in this context, but the inverse function.

tan(x)=y
Arctan(y)=x
With whatever restrictions are necessary so that those are functions and not just relations.
 
  • Like
Likes Voltux

Similar threads

Why Is My Argument Calculation for Complex Number Incorrect?
  • · Replies 14 ·
Replies
14
Views
2K
Question about arctan addition
  • · Replies 17 ·
Replies
17
Views
4K
Inverse Trig Functions and Reciprocals
  • · Replies 15 ·
Replies
15
Views
2K
Solving a trigonometric equation with multiples of ##\tan##
  • · Replies 7 ·
Replies
7
Views
2K
To prove a trigonometric identity with tan() and cot()
  • · Replies 2 ·
Replies
2
Views
2K
Solve the equation: ##\tan x ⋅\tan 4x = 1##
  • · Replies 4 ·
Replies
4
Views
2K
Trig Identities - Pre-calculus in a Nutshell - Section 4 Question 1
  • · Replies 24 ·
Replies
24
Views
3K
Computing arctan (inverse tan) function
  • · Replies 10 ·
Replies
10
Views
3K
How Do You Simplify Trigonometric Expressions Using Basic Identities?
  • · Replies 5 ·
Replies
5
Views
2K
Trigonometry: if a = sinx+cosx and b=tanx+cotx, then a(b^2-1)-2 = ?
  • · Replies 6 ·
Replies
6
Views
3K