Final answer:
To find the exact value of cot 2π/3, determine the cosine and sine of 2π/3. In the second quadrant, the reference angle is π/3. Using the unit circle, cos π/3 = 1/2 and sin π/3 = √3/2. cot 2π/3 = √3/3.
Step-by-step explanation:
The trigonometric function given is cot 2π/3.
To find the exact value of cot 2π/3, we need to determine the cosine and sine of 2π/3.
Since 2π/3 is in the second quadrant, the reference angle is π - 2π/3 = π/3.
Using the unit circle, we can find that cos π/3 = 1/2 and sin π/3 = √3/2.
Hence, cot 2π/3 = cos 2π/3 / sin 2π/3 = (1/2) / (√3/2) = 1/√3 = √3/3.