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.

Question

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.

Knowee AI · Accepted Answer

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.

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