Find the Exact Value csc(-330 degrees )

Problem

csc(−330)

Solution

1. Use the property of odd functions to rewrite the expression, noting that csc(−θ)=−csc(θ)

csc(−330)=−csc(330)

2. Find the reference angle for 330 by subtracting it from 360 because it is in the fourth quadrant.

(θ_ref)=360−330=30

3. Determine the sign of the cosecant function in the fourth quadrant. Since sin(θ) is negative in the fourth quadrant, csc(θ) is also negative.

csc(330)=−csc(30)

4. Substitute this back into the expression from step 1.

−csc(330)=−(−csc(30))=csc(30)

5. Evaluate the cosecant of the reference angle using the reciprocal identity csc(θ)=1/sin(θ)

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

Final Answer

csc(−330)=2

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