Find the Exact Value csc(570)

Problem

csc(570)

Solution

1. Find the coterminal angle by subtracting 360 from the given angle to bring it within the standard range of 0 to 360

570−360=210

2. Identify the reciprocal identity for the cosecant function.

csc(210)=1/sin(210)

3. Determine the reference angle for 210 which is located in the third quadrant.

(θ_ref)=210−180=30

4. Evaluate the sine of the angle, noting that sine is negative in the third quadrant.

sin(210)=−sin(30)

sin(210)=−1/2

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

csc(210)=1/(−1/2)=−2

Final Answer

csc(570)=−2

Want more problems? Check here!