Find the Exact Value cot(pi/6)

Problem

cot(π/6)

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 θ=π/6 into the expression.

cot(π/6)=cos(π/6)/sin(π/6)

3. Recall the exact values for the sine and cosine of π/6 (which is 30 from the unit circle.

cos(π/6)=√(,3)/2

sin(π/6)=1/2

4. Simplify the fraction by dividing the two values.

cot(π/6)=√(,3)/2/1/2

cot(π/6)=√(,3)/2⋅2/1

cot(π/6)=√(,3)

Final Answer

cot(π/6)=√(,3)

Want more problems? Check here!