Value of tan 30°: Exact Form 1/√3 & Decimal

How to derive it

In an equilateral triangle of side 2, drop a perpendicular: it splits into two 30°–60°–90° triangles with sides 1, √3 and 2.
tan = opposite ÷ adjacent, so tan 30° = 1/√3.

Angle	sin	cos	tan
15°	(√6 − √2)/4	(√6 + √2)/4	2 − √3
18°	(√5 − 1)/4	√(10 + 2√5)/4	√(25 − 10√5)/5
22.5°	√(2 − √2)/2	√(2 + √2)/2	√2 − 1
30°	1/2	√3/2	1/√3
36°	√(10 − 2√5)/4	(√5 + 1)/4	√(5 − 2√5)
45°	1/√2	1/√2	1
54°	(√5 + 1)/4	√(10 − 2√5)/4	√(25 + 10√5)/5
60°	√3/2	1/2	√3
67.5°	√(2 + √2)/2	√(2 − √2)/2	√2 + 1
72°	√(10 + 2√5)/4	(√5 − 1)/4	√(5 + 2√5)
75°	(√6 + √2)/4	(√6 − √2)/4	2 + √3

For whole-degree values from 0° to 90°, see the trigonometry table.

What is the value of tan 30°?

1/√3, which is about 0.5774.

What is tan 30° in radians?

30° is π/6 radians, so tan(π/6) = 1/√3.

Is tan 30° equal to cot 60°?

Yes. tan θ = cot(90° − θ), so tan 30° = cot 60°.