What is tan(π/6)?

What is tan(π/6)?

• A. √3
• B. √3/3
• C. 1
• D. 0

Answer: (B)

Tangent is the ratio of the opposite side to the adjacent side in a right triangle, or on the unit circle tan θ = sin θ / cos θ. For the angle π/6 (30°), the standard 30-60-90 triangle gives opposite = 1 and adjacent = √3, so tan(π/6) = 1/√3. This is often written as √3/3 after rationalizing the denominator. You can also see it from sine and cosine values: sin(π/6) = 1/2 and cos(π/6) = √3/2, so tan(π/6) = (1/2)/(√3/2) = 1/√3 = √3/3.

Tangent is the ratio of the opposite side to the adjacent side in a right triangle, or on the unit circle tan θ = sin θ / cos θ. For the angle π/6 (30°), the standard 30-60-90 triangle gives opposite = 1 and adjacent = √3, so tan(π/6) = 1/√3. This is often written as √3/3 after rationalizing the denominator. You can also see it from sine and cosine values: sin(π/6) = 1/2 and cos(π/6) = √3/2, so tan(π/6) = (1/2)/(√3/2) = 1/√3 = √3/3.