Find exact value of cosecant function

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To find the exact value of csc^-1((2√3)/3), it can be rewritten as sin^-1(3/(2√3)). The next step involves rationalizing the denominator of sin^-1(3/(2√3)). This leads to the recognition of a well-known sine value. The discussion emphasizes the importance of using parentheses correctly in mathematical expressions. Understanding these transformations is crucial for solving inverse trigonometric functions accurately.
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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?
 
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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.

\displaystyle \frac{3}{2\sqrt{3}}=?
 
Haha, duh! Thanks.
 
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