Find the Exact Value csc(pi/6)

Problem

csc(π/6)

Solution

1. Identify the trigonometric identity for cosecant, which is the reciprocal of the sine function.

csc(θ)=1/sin(θ)

2. Substitute the given angle π/6 into the identity.

csc(π/6)=1/sin(π/6)

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

sin(π/6)=1/2

4. Calculate the final value by taking the reciprocal of 1/2

1/(1/2)=2

Final Answer

csc(π/6)=2

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