Cot 54 Degrees

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

What is cot 54°?

Answer

cot 54° =
√(5 − 2√5) ≈ 0.7265

Angle in radians: 54° = 3π/10. The point of the angle is in quadrant I, where cotangent is positive.

≈ — rounded to 4 decimal places.

cot 54° = cos 54° / sin 54° = (√(10 − 2√5)/4) / ((√5 + 1)/4) = √(5 − 2√5)

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

cot 54° = tan 36° = sin 36° / cos 36° = √(5 − 2√5)

xyOP

P(cos 54°, sin 54°) ≈ (0.5878, 0.8090)

C(cot 54°, 1) ≈ (0.7265, 1) — where line OP meets the line y = 1.

All four functions of 54°
FunctionExact valueDecimal
sin 54°(√5 + 1)/4≈ 0.8090
cos 54°√(10 − 2√5)/4≈ 0.5878
tan 54°√(25 + 10√5)/5≈ 1.3764
cot 54°√(5 − 2√5)≈ 0.7265

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
51°≈ 0.8098
52°≈ 0.7813
53°≈ 0.7536
54°√(5 − 2√5)
55°≈ 0.7002
56°≈ 0.6745
57°≈ 0.6494

FAQ

What is cot 54°?

cot 54° = √(5 − 2√5) ≈ 0.7265

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 1.4841 for cot 54?

The calculator is in radian mode (RAD): it takes cot 54 as the cotangent of 54 radians, cot 54 rad ≈ 1.4841. Switch it to degrees (DEG): cot 54° = √(5 − 2√5) ≈ 0.7265. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also