Find exact value of cosecant function

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SUMMARY

The discussion focuses on finding the exact value of the cosecant function, specifically csc-1((2√3)/3). Participants clarify that csc-1(x) can be converted to sin-1(1/x), leading to sin-1(3/(2√3)). The solution involves rationalizing the denominator to identify a well-known sine value. The final steps emphasize the importance of proper notation and simplification in trigonometric functions.

PREREQUISITES
  • Understanding of inverse trigonometric functions
  • Knowledge of rationalizing denominators in fractions
  • Familiarity with sine and cosecant relationships
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the properties of inverse trigonometric functions
  • Learn techniques for rationalizing denominators in trigonometric expressions
  • Explore the unit circle and its relationship to sine and cosecant values
  • Practice solving problems involving inverse sine and cosecant functions
USEFUL FOR

Students studying trigonometry, educators teaching inverse functions, and anyone seeking to improve their understanding of trigonometric identities and simplifications.

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Homework Statement



csc^-1((2sqrt3)/3)

Homework Equations



csc^-1((2sqrt3)/3) = sin^-1(3/(2sqrt3))

The Attempt at a Solution



My Math Lab says I am supposed to use the equivalent sine function, so then I got sin^-1(3/2sqrt3). Then what do I do?
 
Last edited:
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veganazi said:

Homework Statement



csc^-1(2sqrt3/3)


Homework Equations



csc^-1(2sqrt3/3) = sin^-1(3/2sqrt3)


The Attempt at a Solution



My Math Lab says I am supposed to use the equivalent sine function, so then I got sin^-1(3/2sqrt3). Then what do I do?
Use enough parentheses for this to be correct.

csc^-1(2sqrt3/3) = sin^-1(3/(2sqrt3))

Then rationalize the denominator so you can recognize a well-known value of the sine.

[itex]\displaystyle \frac{3}{2\sqrt{3}}=?[/itex]
 
Haha, duh! Thanks.
 
Last edited:

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