The tangent of pi over 3 (tan(π/3)) is equal to the square root of 3.
Here's how to understand and calculate it:
- Understanding π/3: π/3 radians is equivalent to 60 degrees.
- The Unit Circle: Consider a 30-60-90 triangle. In a unit circle, the coordinates of the point corresponding to π/3 are (1/2, √3/2).
- Tangent Definition: Tangent is defined as sine divided by cosine, or opposite over adjacent in a right triangle. In the unit circle context, tan(θ) = y/x.
- Calculation: Therefore, tan(π/3) = (√3/2) / (1/2) = √3.
So, tan(π/3) = √3, which is approximately 1.732.
