Simplify 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. Evaluate the sine of π/3 using the unit circle or special triangles.

sin(π/3)=√(,3)/2

4. Simplify the fraction by taking the reciprocal.

1/√(,3)/2=2/√(,3)

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

(2⋅√(,3))/(√(,3)⋅√(,3))=(2√(,3))/3

Final Answer

csc(π/3)=(2√(,3))/3

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