Find the Exact Value csc(180)

Problem

csc(180^∘)

Solution

1. Identify the definition of the cosecant function in terms of the sine function.

csc(θ)=1/sin(θ)

2. Evaluate the sine of 180^∘ using the unit circle.

sin(180^∘)=0

3. Substitute the value of sin(180^∘) into the cosecant expression.

csc(180^∘)=1/0

4. Determine the existence of the value. Since division by zero is undefined, the cosecant of 180^∘ does not exist.

Final Answer

csc(180^∘)=undefined

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