Simplify csc(120)

Problem

csc(120)

Solution

1. Identify the relationship between the cosecant function and the sine function using the reciprocal identity.

csc(120)=1/sin(120)

2. Determine the reference angle for 120 Since 120 is in the second quadrant, the reference angle is 180−120=60

sin(120)=sin(60)

3. Substitute the known exact value for sin(60) which is √(,3)/2

sin(120)=√(,3)/2

4. Calculate the reciprocal of the sine value to find the cosecant.

csc(120)=1/√(,3)/2

5. Simplify the fraction by multiplying by the reciprocal.

csc(120)=2/√(,3)

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

csc(120)=(2√(,3))/3

Final Answer

csc(120)=(2√(,3))/3

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