Cot 144 Degrees

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

What is cot 144°?

Answer

cot 144° =
−√(25 + 10√5)/5 ≈ −1.3764

Angle in radians: 144° = 4π/5. The point of the angle is in quadrant II, where cotangent is negative.

≈ — rounded to 4 decimal places.

cot 144° = cot(180° − 36°) = −cot 36° = −√(25 + 10√5)/5

cot 144° = cos 144° / sin 144° = (−(√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 144°, sin 144°) ≈ (−0.8090, 0.5878)

C(cot 144°, 1) ≈ (−1.3764, 1) — where line OP meets the line y = 1.

All four functions of 144°
FunctionExact valueDecimal
sin 144°√(10 − 2√5)/4≈ 0.5878
cos 144°−(√5 + 1)/4≈ −0.8090
tan 144°−√(5 − 2√5)≈ −0.7265
cot 144°−√(25 + 10√5)/5≈ −1.3764

Reference angle: cot 36° = √(25 + 10√5)/5

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
135°−1
140°≈ −1.1918
142°≈ −1.2799
144°−√(25 + 10√5)/5
145°≈ −1.4281
150°−√3
159°≈ −2.6051

FAQ

What is cot 144°?

cot 144° = −√(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 −1.7742 for cot 144?

The calculator is in radian mode (RAD): it takes cot 144 as the cotangent of 144 radians, cot 144 rad ≈ −1.7742. Switch it to degrees (DEG): cot 144° = −√(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