Cot 72 Degrees

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

What is cot 72°?

Answer

cot 72° =
√(25 − 10√5)/5 ≈ 0.3249

Angle in radians: 72° = 2π/5. The point of the angle is in quadrant I, where cotangent is positive.

≈ — rounded to 4 decimal places.

cot 72° = cos 72° / sin 72° = ((√5 − 1)/4) / (√(10 + 2√5)/4) = √(25 − 10√5)/5

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

cot 72° = tan 18° = sin 18° / cos 18° = √(25 − 10√5)/5

xyOP

P(cos 72°, sin 72°) ≈ (0.3090, 0.9511)

C(cot 72°, 1) ≈ (0.3249, 1) — where line OP meets the line y = 1.

All four functions of 72°
FunctionExact valueDecimal
sin 72°√(10 + 2√5)/4≈ 0.9511
cos 72°(√5 − 1)/4≈ 0.3090
tan 72°√(5 + 2√5)≈ 3.0777
cot 72°√(25 − 10√5)/5≈ 0.3249

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
69°≈ 0.3839
70°≈ 0.3640
71°≈ 0.3443
72°√(25 − 10√5)/5
73°≈ 0.3057
74°≈ 0.2867
75°2 − √3

FAQ

What is cot 72°?

cot 72° = √(25 − 10√5)/5 ≈ 0.3249

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 −3.8107 for cot 72?

The calculator is in radian mode (RAD): it takes cot 72 as the cotangent of 72 radians, cot 72 rad ≈ −3.8107. Switch it to degrees (DEG): cot 72° = √(25 − 10√5)/5 ≈ 0.3249. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also