Find the Exact Value csc(-30)

Problem

csc(−30)

Solution

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

csc(−30)=−csc(30)

2. Use the reciprocal identity to express cosecant in terms of sine, where csc(θ)=1/sin(θ)

−csc(30)=−1/sin(30)

3. Substitute the known value for sin(30) which is 1/2

−1/sin(30)=−1/(1/2)

4. Simplify the fraction by multiplying by the reciprocal.

−1⋅2=−2

Final Answer

csc(−30)=−2

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