Find the Exact Value csc(330)

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.

In Quadrant IV, *sin(θ)<0⇒csc(θ)<0

3. Apply the trigonometric identity relating cosecant to sine.

csc(330)=1/sin(330)

4. Substitute the value of the sine of the reference angle, keeping the negative sign for the fourth quadrant.

sin(330)=−sin(30)=−1/2

5. Calculate the reciprocal to find the final value.

csc(330)=1/(−1/2)=−2

Final Answer

csc(330)=−2

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