Use the special triangle shown on the unit circle to find the tangent of pie/3

Answer 1

In the special triangle on the unit circle, we have a 30-60-90 triangle with side lengths 1, √3, and 2.

Since we are looking for the tangent of π/3, which corresponds to the angle 60 degrees in the unit circle, we will use the side lengths of the triangle opposite and adjacent to the angle 60 degrees.

The tangent of an angle in a right triangle is defined as opposite/adjacent. Therefore, the tangent of π/3 is:

tan(π/3) = opposite/adjacent
tan(60 degrees) = √3/1
tan(60 degrees) = √3

Therefore, the tangent of π/3 is √3.