Find the Exact Value csc(-180 degrees )

Problem

csc(−180)

Solution

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

csc(θ)=1/sin(θ)

2. Substitute the given angle into the identity.

csc(−180)=1/sin(−180)

3. Evaluate the sine of −180 using the unit circle or the property sin(−θ)=−sin(θ)

sin(−180)=−sin(180)

sin(180)=0

sin(−180)=0

4. Determine the value of the expression by substituting the sine value back into the fraction.

csc(−180)=1/0

5. Conclude that since division by zero is not defined, the value does not exist.

Final Answer

csc(−180)=undefined

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