High School What is the difference between arcsin and inverse sin?

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SUMMARY

The terms "arcsin" and "inverse sin" refer to the same mathematical function, specifically the inverse of the sine function. Similarly, "arccos" and "inverse cos," as well as "arctan" and "inverse tan," are interchangeable terms for their respective inverse functions. However, it is crucial to note that the sine and cosine functions are not globally invertible; they are only invertible within specific intervals: sine on [-π/2, π/2] and cosine on [0, π]. This distinction is essential for understanding the behavior of these functions and their inverses.

PREREQUISITES
  • Understanding of trigonometric functions and their properties
  • Knowledge of function inverses and their definitions
  • Familiarity with the concept of function domains and ranges
  • Basic grasp of mathematical notation and intervals
NEXT STEPS
  • Study the properties of trigonometric functions and their inverses
  • Learn about the domains and ranges of arcsin, arccos, and arctan
  • Explore the graphical representations of sine, cosine, and their inverse functions
  • Investigate the applications of inverse trigonometric functions in solving equations
USEFUL FOR

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

tony873004
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What's the difference between arcsin and inverse sin?
arccos and inverse cos?
arctan and inverse tan?
 
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nothing they are the same...different ways of saying the same thing.
 
tony873004 said:
What's the difference between arcsin and inverse sin?
arccos and inverse cos?
arctan and inverse tan?

None,none,none...There is a trick though.For sine and cosine for example,defined on R,the rule f:A->B,f-1:B->A would not apply,since
\sin x:R\rightarrow [-1,+1]
\cos x:R\rightarrow [-1,-1]
\arcsin x:[-1,+1]\rightarrow [-\frac{\pi}{2},+\frac{\pi}{2}]
\arccos x:[-1,+1]\rightarrow [0,\pi]
,so the 'arcsine' and 'arccosine' are the inverse functions of 'sine' respectively 'cosine',BUT SINE X is inveritble only on the interval [-\frac{\pi}{2},+\frac{\pi}{2}],and similar for COSINE X.
I'll let u work out the other examples for circular trigonometric functions:tan,cotan,sec,cosec.

Daniel.
 

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