Find the Value Using the Unit Circle csc(60 degrees )

Problem

csc(60)

Solution

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

csc(θ)=1/sin(θ)

2. Determine the sine value for the given angle using the unit circle coordinates at 60

sin(60)=√(,3)/2

3. Substitute the sine value into the reciprocal identity to find the cosecant.

csc(60)=1/√(,3)/2

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

csc(60)=2/√(,3)

5. 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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