Simplify arccsc(-2/( square root of 3))

Problem

arccsc(−2/√(,3))

Solution

1. Identify the definition of the inverse cosecant function. The expression y=arccsc(x) is equivalent to csc(y)=x where y is in the range [−π/2,0)∪(0,π/2]

2. Rewrite the equation in terms of the sine function using the reciprocal identity csc(y)=1/sin(y)

csc(y)=−2/√(,3)

sin(y)=−√(,3)/2

3. Determine the angle y within the interval [−π/2,π/2] that satisfies the sine equation. Since sin(π/3)=√(,3)/2 and the sine function is odd, sin(−π/3)=−√(,3)/2

y=−π/3

Final Answer

arccsc(−2/√(,3))=−π/3

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