Cot 390 Degrees

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

What is cot 390°?

Answer

cot 390° =
√3 ≈ 1.7321

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

≈ — rounded to 4 decimal places.

cot 390° = cot(390° − 360°) = cot 30°

cot 390° = cos 390° / sin 390° = (√3/2) / (1/2) = √3

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

cot 30° = (√3/2) / (1/2) = √3

xyOP

P(cos 390°, sin 390°) ≈ (0.8660, 0.5)

C(cot 390°, 1) ≈ (1.7321, 1) — where line OP meets the line y = 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: cot 30° = √3

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
345°−2 − √3
355°≈ −11.4301
360°undefined
390°√3
400°≈ 1.1918
450°0
540°undefined

FAQ

What is cot 390°?

cot 390° = √3 ≈ 1.7321

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: cot 390° = √3 ≈ 1.7321.

Why does a calculator show 2.1104 for cot 390?

The calculator is in radian mode (RAD): it takes cot 390 as the cotangent of 390 radians, cot 390 rad ≈ 2.1104. Switch it to degrees (DEG): cot 390° = √3 ≈ 1.7321. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also