What Is the Opposite of a Trig Function?

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SUMMARY

The discussion centers on the terminology surrounding trigonometric functions and their inverses. The term "inverse" is correctly identified as the opposite of a trigonometric function, specifically referring to arcsine (arcsin) and arccosine (arccos). Participants clarify that while "inverse" can imply a reciprocal in some contexts, in trigonometry, it denotes a function that undoes the effect of the original function. The confusion arises from the notation, particularly the use of -1, which can represent both inverse functions and reciprocals.

PREREQUISITES
  • Understanding of basic trigonometric functions such as sine and cosine
  • Familiarity with the concept of inverse functions
  • Knowledge of mathematical notation, particularly exponents
  • Basic algebra skills, including manipulation of fractions and functions
NEXT STEPS
  • Study the properties and graphs of inverse trigonometric functions like arcsin and arccos
  • Learn about the restricted domains of trigonometric functions for their inverses
  • Explore the differences between inverse functions and reciprocal functions
  • Practice solving equations involving inverse trigonometric functions
USEFUL FOR

Students of mathematics, educators teaching trigonometry, and anyone seeking to clarify the concepts of inverse functions in trigonometry.

Jules18
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"Inverse" trig?

I'm trying to think of a word that describes the opposite of a trig function.
It's like inverse, but I know that's not exactly the right word because inverse means literally "1 over" the function.
It's the type of function you get when you press "2nd function" before you press Sin or Cos or whatever.

I'm pretty sure it starts with "i" ... does anyone know what I'm talking about? :confused:
 
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I think you are looking for the word "inverse" and confusing notation with -1. 1 over something is usually called the reciprocal and is also indicated by a -1 exponent (x-1 = 1/x).
Sometimes a -1 does mean inverse. The inverse of sine (with a restricted domain) is arcsin x = sin-1x ≠ (sin x)-1 = 1/sinx.
 


ahhhh okay yeah I always confuse those two
 

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