Cos 390 Degrees

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

What is cos 390°?

Answer

cos 390° =
√3/2 ≈ 0.8660

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

≈ — rounded to 4 decimal places.

cos 390° = cos(390° − 360°) = cos 30°

P(cos 390°, sin 390°) = (√3/2, 1/2)

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

cos 30° = √(1 − 1/4) = √3/2

xyOP

P(cos 390°, sin 390°) ≈ (0.8660, 0.5)

Highlighted: the projection on the x-axis — cosine, x ≈ 0.8660.

+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: cos 30° = √3/2

See Also

Recalculate with different values ↑

Cosine of nearby angles

Anglecos
345°(√6 + √2)/4
355°≈ 0.9962
360°1
390°√3/2
400°≈ 0.7660
450°0
540°−1

FAQ

What is cos 390°?

cos 390° = √3/2 ≈ 0.8660

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: cos 390° = √3/2 ≈ 0.8660.

Why does a calculator show 0.9037 for cos 390?

The calculator is in radian mode (RAD): it takes cos 390 as the cosine of 390 radians, cos 390 rad ≈ 0.9037. Switch it to degrees (DEG): cos 390° = √3/2 ≈ 0.8660. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also