Find the Exact Value csc(360)

Problem

csc(360)

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(360)=1/sin(360)

3. Evaluate the sine of 360 using the unit circle, where 360 corresponds to the point (1,0)

sin(360)=0

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

csc(360)=1/0

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

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Final Answer

csc(360)=undefined

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