Find the exact value of cotangent, 120, degreescot120 ∘ in simplest form with a rational denominator

To find the exact value of cot(120°), we first need to understand that cotangent is the reciprocal of tangent.

Step 1: Convert the degrees to radians. 120 degrees is equal to 2π/3 radians.

Step 2: Find the tangent of the angle. tan(120°) = tan(180° - 60°) = -tan(60°) = -√3

Step 3: Find the cotangent of the angle. cot(120°) = 1/tan(120°) = 1/(-√3) = -1/√3

Step 4: Rationalize the denominator. Multiply the numerator and the denominator by √3 to get -√3/3.

So, cot(120°) = -√3/3.