Find the Exact Value csc(540)

Problem

csc(540)

Solution

1. Subtract multiples of 360 to find the coterminal angle within the standard range of 0 to 360

540−360=180

2. Identify the trigonometric identity for cosecant in terms of sine.

csc(θ)=1/sin(θ)

3. Evaluate the sine of the coterminal angle.

sin(180)=0

4. Determine the value of the cosecant function at this angle. Since the sine of 180 is zero, the reciprocal is undefined.

csc(180)=1/0

Final Answer

csc(540)=Undefined

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