Tan 30 Degrees

Sin, Cos, Tan, Cot of an Angle
Function
Angle (°)

What is tan 30°?

Answer

tan 30° =
√3/3 ≈ 0.5774

Angle in radians: 30° = π/6. The point of the angle is in quadrant I, where tangent is positive.

≈ — rounded to 4 decimal places.

tan 30° = sin 30° / cos 30° = (1/2) / (√3/2) = √3/3

Half of an equilateral triangle with side 1: the hypotenuse is 1 and the leg opposite 30° is 1/2.

tan 30° = (1/2) / (√3/2) = 1/√3 = √3/3

xyOP

P(cos 30°, sin 30°) ≈ (0.8660, 0.5)

T(1, tan 30°) ≈ (1, 0.5774) — where line OP meets the line x = 1.

All four functions of 30°
FunctionExact valueDecimal
sin 30°1/20.5
cos 30°√3/2≈ 0.8660
tan 30°√3/3≈ 0.5774
cot 30°√3≈ 1.7321

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
27°≈ 0.5095
28°≈ 0.5317
29°≈ 0.5543
30°√3/3
31°≈ 0.6009
32°≈ 0.6249
33°≈ 0.6494

FAQ

What is tan 30°?

tan 30° = √3/3 ≈ 0.5774

How to remember sin 30°, sin 45° and sin 60°?

Write them as √1/2, √2/2, √3/2: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2. Cosines are the same numbers in reverse order: cos 30° = √3/2, cos 45° = √2/2, cos 60° = 1/2; tan = sin / cos and cot = cos / sin. Here: tan 30° = √3/3 ≈ 0.5774.

Why does a calculator show −6.4053 for tan 30?

The calculator is in radian mode (RAD): it takes tan 30 as the tangent of 30 radians, tan 30 rad ≈ −6.4053. Switch it to degrees (DEG): tan 30° = √3/3 ≈ 0.5774. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also