Find the Exact Value csc(150 degrees )

Problem

csc(150)

Solution

1. Identify the reference angle for 150 Since 150 is in the second quadrant, the reference angle is calculated as 180−150=30

2. Determine the sign of the cosecant function in the second quadrant. In the second quadrant, the sine function is positive, and since csc(θ)=1/sin(θ) the cosecant function is also positive.

3. Apply the reference angle property.

csc(150)=csc(30)

4. Evaluate the cosecant of the reference angle using the reciprocal identity.

csc(30)=1/sin(30)

5. Substitute the known value sin(30)=1/2

csc(30)=1/(1/2)=2

Final Answer

csc(150)=2

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