Find the Exact Value csc(-390)

Problem

csc(−390)

Solution

1. Find the coterminal angle by adding 360 to the given angle until it falls within the range of 0 to 360

θ=−390+360=−30

θ=−30+360=330

2. Identify the reciprocal identity for the cosecant function.

csc(θ)=1/sin(θ)

3. Determine the reference angle for 330 which is located in Quadrant IV.

(θ_ref)=360−330=30

4. Evaluate the sine of the angle, noting that sine is negative in Quadrant IV.

sin(330)=−sin(30)

sin(330)=−1/2

5. Calculate the cosecant by taking the reciprocal of the sine value.

csc(−390)=1/(−1/2)

csc(−390)=−2

Final Answer

csc(−390)=−2

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