Find the Value Using the Unit Circle csc((11pi)/6)

Problem

csc((11*π)/6)

Solution

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

csc(θ)=1/sin(θ)

2. Locate the angle (11*π)/6 on the unit circle. This angle is in the fourth quadrant.

3. Determine the ycoordinate of the point on the unit circle at (11*π)/6 which represents the sine of the angle.

sin((11*π)/6)=−1/2

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

csc((11*π)/6)=1/(−1/2)

5. Simplify the fraction by multiplying by the reciprocal.

csc((11*π)/6)=−2

Final Answer

csc((11*π)/6)=−2

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