Cot 216 Degrees

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

What is cot 216°?

Answer

cot 216° =
√(25 + 10√5)/5 ≈ 1.3764

Angle in radians: 216° = 6π/5. The point of the angle is in quadrant III, where cotangent is positive.

≈ — rounded to 4 decimal places.

cot 216° = cot(180° + 36°) = cot 36° = √(25 + 10√5)/5

cot 216° = cos 216° / sin 216° = (−(√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 216°, sin 216°) ≈ (−0.8090, −0.5878)

C(cot 216°, 1) ≈ (1.3764, 1) — where line OP meets the line y = 1, on the extension of the ray beyond O (dashed).

All four functions of 216°
FunctionExact valueDecimal
sin 216°−√(10 − 2√5)/4≈ −0.5878
cos 216°−(√5 + 1)/4≈ −0.8090
tan 216°√(5 − 2√5)≈ 0.7265
cot 216°√(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
210°√3
211°≈ 1.6643
215°≈ 1.4281
216°√(25 + 10√5)/5
225°1
227°≈ 0.9325
234°√(5 − 2√5)

FAQ

What is cot 216°?

cot 216° = √(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 −1.0315 for cot 216?

The calculator is in radian mode (RAD): it takes cot 216 as the cotangent of 216 radians, cot 216 rad ≈ −1.0315. Switch it to degrees (DEG): cot 216° = √(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