Cos 30 Degrees

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

What is cos 30°?

Answer

cos 30° =
√3/2 ≈ 0.8660

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

≈ — rounded to 4 decimal places.

P(cos 30°, sin 30°) = (√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 30°, sin 30°) ≈ (0.8660, 0.5)

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

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 ↑

Cosine of nearby angles

Anglecos
27°≈ 0.8910
28°≈ 0.8829
29°≈ 0.8746
30°√3/2
31°≈ 0.8572
32°≈ 0.8480
33°≈ 0.8387

FAQ

What is cos 30°?

cos 30° = √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 30° = √3/2 ≈ 0.8660.

Why does a calculator show 0.1543 for cos 30?

The calculator is in radian mode (RAD): it takes cos 30 as the cosine of 30 radians, cos 30 rad ≈ 0.1543. Switch it to degrees (DEG): cos 30° = √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