Simplify csc(pi/6)

Problem

csc(π/6)

Solution

1. Identify the definition of the cosecant function in terms of the sine function.

csc(θ)=1/sin(θ)

2. Substitute the given angle into the identity.

csc(π/6)=1/sin(π/6)

3. Evaluate the sine of the angle using the unit circle or special triangles, where sin(π/6)=1/2

csc(π/6)=1/(1/2)

4. Simplify the complex fraction by multiplying by the reciprocal.

csc(π/6)=2

Final Answer

csc(π/6)=2

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