Find the Exact Value csc(-60 degrees )

Problem

csc(−60)

Solution

1. Apply the odd function property for the cosecant function, which states that csc(−θ)=−csc(θ)

csc(−60)=−csc(60)

2. Use the reciprocal identity to express cosecant in terms of sine.

−csc(60)=−1/sin(60)

3. Substitute the known value for sin(60) which is √(,3)/2

−1/sin(60)=−1/√(,3)/2

4. Simplify the fraction by multiplying by the reciprocal.

−1/√(,3)/2=−2/√(,3)

5. Rationalize the denominator by multiplying the numerator and denominator by √(,3)

−2/√(,3)⋅√(,3)/√(,3)=−(2√(,3))/3

Final Answer

csc(−60)=−(2√(,3))/3

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