Find the Exact Value csc(390)

Problem

csc(390)

Solution

1. Find the coterminal angle by subtracting 360 from the given angle to find an equivalent angle within the first rotation.

390−360=30

2. Apply the reciprocal identity for the cosecant function, which states that csc(θ)=1/sin(θ)

csc(390)=csc(30)

csc(30)=1/sin(30)

3. Substitute the known value for sin(30) which is 1/2 based on the unit circle or a 30−60−90 reference triangle.

sin(30)=1/2

4. Simplify the fraction by calculating the reciprocal of 1/2

1/(1/2)=2

Final Answer

csc(390)=2

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