Find the Exact Value csc(330 degrees )

Problem

csc(330)

Solution

1. Identify the reference angle by finding the difference between 330 and 360 since the angle is in the fourth quadrant.

360−330=30

2. Determine the sign of the cosecant function in the fourth quadrant. Since csc(θ)=1/sin(θ) and sine is negative in the fourth quadrant, the result will be negative.

csc(330)=−csc(30)

3. Apply the reciprocal identity for cosecant.

csc(30)=1/sin(30)

4. Substitute the known value sin(30)=1/2 into the expression.

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

5. Combine the value with the negative sign determined in step 2.

csc(330)=−2

Final Answer

csc(330)=−2

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