Find the Exact Value csc(-pi/6)

Problem

csc(−π/6)

Solution

1. Identify the trigonometric identity for negative angles. The cosecant function is odd, meaning csc(−x)=−csc(x)

csc(−π/6)=−csc(π/6)

2. Relate the cosecant function to the sine function using the reciprocal identity csc(x)=1/sin(x)

−csc(π/6)=−1/sin(π/6)

3. Determine the exact value of sin(π/6) from the unit circle or special triangles.

sin(π/6)=1/2

4. Substitute the value back into the expression and simplify the fraction.

−1/1/2=−2

Final Answer

csc(−π/6)=−2

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