Find the Exact Value csc(3pi)

Problem

csc(3*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 3*π into the expression.

csc(3*π)=1/sin(3*π)

3. Determine the value of sin(3*π) using the unit circle or periodicity.

sin(3*π)=sin(3*π−2*π)

sin(3*π)=sin(π)

sin(π)=0

4. Evaluate the expression by substituting the value of the sine function.

csc(3*π)=1/0

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

Final Answer

csc(3*π)=undefined

Want more problems? Check here!