Tan 390 Degrees

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

What is tan 390°?

Answer

tan 390° =
√3/3 ≈ 0.5774

Angle in radians: 390° = 13π/6. 390° = 360° + 30° — a full turn plus 30°, quadrant I, where tangent is positive.

≈ — rounded to 4 decimal places.

tan 390° = tan(390° − 360°) = tan 30°

tan 390° = sin 390° / cos 390° = (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 390°, sin 390°) ≈ (0.8660, 0.5)

T(1, tan 390°) ≈ (1, 0.5774) — where line OP meets the line x = 1.

+1 turn: the drawing shows 30°.

All four functions of 390°
FunctionExact valueDecimal
sin 390°1/20.5
cos 390°√3/2≈ 0.8660
tan 390°√3/3≈ 0.5774
cot 390°√3≈ 1.7321

Reference angle: tan 30° = √3/3

See Also

Recalculate with different values ↑

Tangent of nearby angles

Angletan
345°√3 − 2
355°≈ −0.0875
360°0
390°√3/3
400°≈ 0.8391
450°undefined
540°0

FAQ

What is tan 390°?

tan 390° = √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 390° = √3/3 ≈ 0.5774.

Why does a calculator show 0.4739 for tan 390?

The calculator is in radian mode (RAD): it takes tan 390 as the tangent of 390 radians, tan 390 rad ≈ 0.4739. Switch it to degrees (DEG): tan 390° = √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