Simplify csc(60)

Problem

csc(60)

Solution

1. Identify the definition of the cosecant function as the reciprocal of the sine function.

csc(60)=1/sin(60)

2. Recall the exact value of sin(60) from the unit circle or a special 30−60−90 triangle.

sin(60)=√(,3)/2

3. Substitute the value of the sine function into the reciprocal expression.

csc(60)=1/√(,3)/2

4. Simplify the fraction by multiplying by the reciprocal of the denominator.

csc(60)=2/√(,3)

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

csc(60)=(2√(,3))/3

Final Answer

csc(60)=(2√(,3))/3

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