Find the Exact Value csc(-pi)

Problem

csc(−π)

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 definition.

csc(−π)=1/sin(−π)

3. Evaluate the sine of the angle −π On the unit circle, the angle −π radians (or −180 corresponds to the point (−1,0)

sin(−π)=0

4. Determine the value of the fraction. Since the denominator is zero, the expression is undefined.

1/0=undefined

Final Answer

csc(−π)=undefined

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