Find the exact value csc^-1(2)

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The function csc^-1(x) is equivalent to arcsin(1/x). Therefore, csc^-1(2) is equal to arcsin(1/2).

To find the value of arcsin(1/2), we need to find the angle whose sine equals 1/2. Looking at the unit circle, we find that this angle is π/6 or 30 degrees.

Therefore, csc^-1(2) = arcsin(1/2) = π/6 or 30 degrees.

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