Find the Exact Value cot(3pi)

Problem

cot(3*π)

Solution

1. Identify the definition of the cotangent function in terms of sine and cosine.

cot(θ)=cos(θ)/sin(θ)

2. Substitute the given angle 3*π into the expression.

cot(3*π)=cos(3*π)/sin(3*π)

3. Determine the values of the trigonometric functions at 3*π by using the unit circle or periodicity. Since 3*π is coterminal with π

cos(3*π)=−1

sin(3*π)=0

4. Evaluate the fraction by substituting the values.

cot(3*π)=(−1)/0

5. Conclude that since the denominator is zero, the expression is undefined.

Final Answer

cot(3*π)=undefined

Want more problems? Check here!