Find the Exact Value csc(6pi)

Problem

csc(6*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 6*π into the expression.

csc(6*π)=1/sin(6*π)

3. Determine the value of sin(6*π) by noting that 6*π is a multiple of 2*π

sin(6*π)=sin(0)=0

4. Evaluate the fraction by substituting the sine value back into the cosecant expression.

csc(6*π)=1/0

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

Final Answer

csc(6*π)=undefined

Want more problems? Check here!