Cot 18 Degrees

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

What is cot 18°?

Answer

cot 18° =
√(5 + 2√5) ≈ 3.0777

Angle in radians: 18° = π/10. The point of the angle is in quadrant I, where cotangent is positive.

≈ — rounded to 4 decimal places.

cot 18° = cos 18° / sin 18° = (√(10 + 2√5)/4) / ((√5 − 1)/4) = √(5 + 2√5)

Regular pentagon (golden ratio): cos 36° = (√5 + 1)/4.

cot 18° = cos 18° / sin 18° = √(5 + 2√5)

xyOP

P(cos 18°, sin 18°) ≈ (0.9511, 0.3090)

C(cot 18°, 1) ≈ (3.0777, 1) — where line OP meets the line y = 1; C is beyond the drawing, the arrow points to it.

All four functions of 18°
FunctionExact valueDecimal
sin 18°(√5 − 1)/4≈ 0.3090
cos 18°√(10 + 2√5)/4≈ 0.9511
tan 18°√(25 − 10√5)/5≈ 0.3249
cot 18°√(5 + 2√5)≈ 3.0777

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
15°2 + √3
16°≈ 3.4874
17°≈ 3.2709
18°√(5 + 2√5)
19°≈ 2.9042
20°≈ 2.7475
21°≈ 2.6051

FAQ

What is cot 18°?

cot 18° = √(5 + 2√5) ≈ 3.0777

How are sin 18° and cos 72° related?

They are equal: sin α = cos(90° − α), and 18° + 72° = 90°. So sin 18° = cos 72° = (√5 − 1)/4, cos 18° = sin 72° = √(10 + 2√5)/4, and tan 18° = cot 72° = √(25 − 10√5)/5.

Why does a calculator show −0.8793 for cot 18?

The calculator is in radian mode (RAD): it takes cot 18 as the cotangent of 18 radians, cot 18 rad ≈ −0.8793. Switch it to degrees (DEG): cot 18° = √(5 + 2√5) ≈ 3.0777. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also