Simplify csc((2 square root of 3)/3)

Problem

csc((2√(,3))/3)

Solution

1. Identify the input value of the cosecant function. The expression is csc((2√(,3))/3)

2. Rationalize the denominator of the input to see if it matches a known value. Multiplying the numerator and denominator by √(,3) gives:

(2√(,3))/3=(2√(,3))/(√(,3)√(,3))=2/√(,3)

3. Evaluate the cosecant function. The cosecant is the reciprocal of the sine function:

csc(x)=1/sin(x)

4. Determine if the input is an angle or a value. In the context of "Simplify csc(θ), the expression (2√(,3))/3 is the argument (angle) in radians. Since (2√(,3))/3≈1.1547 which is not a standard multiple of π the expression is already in its simplest exact form.

Final Answer

csc((2√(,3))/3)=csc((2√(,3))/3)

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