Find the Exact Value csc(60 degrees )

Problem

csc(60)

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(60)=1/sin(60)

3. Recall the exact value of the sine of 60 from the unit circle or a special right triangle.

sin(60)=√(,3)/2

4. Substitute the value of the sine function back into the expression.

csc(60)=1/√(,3)/2

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

csc(60)=2/√(,3)

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

csc(60)=(2√(,3))/3

Final Answer

csc(60)=(2√(,3))/3

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