Cot 108 Degrees

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

What is cot 108°?

Answer

cot 108° =
−√(25 − 10√5)/5 ≈ −0.3249

Angle in radians: 108° = 3π/5. The point of the angle is in quadrant II, where cotangent is negative.

≈ — rounded to 4 decimal places.

cot 108° = cot(180° − 72°) = −cot 72° = −√(25 − 10√5)/5

cot 108° = cos 108° / sin 108° = (−(√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 108°, sin 108°) ≈ (−0.3090, 0.9511)

C(cot 108°, 1) ≈ (−0.3249, 1) — where line OP meets the line y = 1.

All four functions of 108°
FunctionExact valueDecimal
sin 108°√(10 + 2√5)/4≈ 0.9511
cos 108°−(√5 − 1)/4≈ −0.3090
tan 108°−√(5 + 2√5)≈ −3.0777
cot 108°−√(25 − 10√5)/5≈ −0.3249

Reference angle: cot 72° = √(25 − 10√5)/5

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
101°≈ −0.1944
105°√3 − 2
106°≈ −0.2867
108°−√(25 − 10√5)/5
110°≈ −0.3640
120°−√3/3
125°≈ −0.7002

FAQ

What is cot 108°?

cot 108° = −√(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 0.4052 for cot 108?

The calculator is in radian mode (RAD): it takes cot 108 as the cotangent of 108 radians, cot 108 rad ≈ 0.4052. Switch it to degrees (DEG): cot 108° = −√(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