Evaluate csc(pi/3)

Problem

csc(π/3)

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/3)=1/sin(π/3)

3. Recall the exact value of the sine of π/3 from the unit circle or a special right triangle.

sin(π/3)=√(,3)/2

4. Calculate the reciprocal of the sine value.

csc(π/3)=1/√(,3)/2

csc(π/3)=2/√(,3)

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

csc(π/3)=(2√(,3))/3

Final Answer

csc(π/3)=(2√(,3))/3

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