Cot 36 Degrees

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

What is cot 36°?

Answer

cot 36° =
√(25 + 10√5)/5 ≈ 1.3764

Angle in radians: 36° = π/5. The point of the angle is in quadrant I, where cotangent is positive.

≈ — rounded to 4 decimal places.

cot 36° = cos 36° / sin 36° = ((√5 + 1)/4) / (√(10 − 2√5)/4) = √(25 + 10√5)/5

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

cot 36° = cos 36° / sin 36° = √(25 + 10√5)/5

xyOP

P(cos 36°, sin 36°) ≈ (0.8090, 0.5878)

C(cot 36°, 1) ≈ (1.3764, 1) — where line OP meets the line y = 1.

All four functions of 36°
FunctionExact valueDecimal
sin 36°√(10 − 2√5)/4≈ 0.5878
cos 36°(√5 + 1)/4≈ 0.8090
tan 36°√(5 − 2√5)≈ 0.7265
cot 36°√(25 + 10√5)/5≈ 1.3764

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
33°≈ 1.5399
34°≈ 1.4826
35°≈ 1.4281
36°√(25 + 10√5)/5
37°≈ 1.3270
38°≈ 1.2799
39°≈ 1.2349

FAQ

What is cot 36°?

cot 36° = √(25 + 10√5)/5 ≈ 1.3764

How are sin 36° and cos 54° related?

They are equal: sin α = cos(90° − α), and 36° + 54° = 90°. So sin 36° = cos 54° = √(10 − 2√5)/4, cos 36° = sin 54° = (√5 + 1)/4, and tan 36° = cot 54° = √(5 − 2√5).

Why does a calculator show 0.1290 for cot 36?

The calculator is in radian mode (RAD): it takes cot 36 as the cotangent of 36 radians, cot 36 rad ≈ 0.1290. Switch it to degrees (DEG): cot 36° = √(25 + 10√5)/5 ≈ 1.3764. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also