Find the exact value of the following expression: tan(2π/3)

To find the exact value of tan(2π/3), we start by recognizing the position of the angle on the unit circle.

The angle 2π/3 is located in the second quadrant. We can express it in terms of a reference angle:

• The reference angle is found by subtracting π/2 from 2π/3:
• π – 2π/3 = π/3

Next, we recall the tangent function’s behavior in different quadrants. In the second quadrant, the sine value is positive while the cosine value is negative. Thus,:

• tan(θ) = sin(θ) / cos(θ)
• For our angle, we can use the reference angle π/3:
• tan(2π/3) = -tan(π/3)