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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