Cot 234 Degrees

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

What is cot 234°?

Answer

cot 234° =
√(5 − 2√5) ≈ 0.7265

Angle in radians: 234° = 13π/10. The point of the angle is in quadrant III, where cotangent is positive.

≈ — rounded to 4 decimal places.

cot 234° = cot(180° + 54°) = cot 54° = √(5 − 2√5)

cot 234° = cos 234° / sin 234° = (−√(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 234°, sin 234°) ≈ (−0.5878, −0.8090)

C(cot 234°, 1) ≈ (0.7265, 1) — where line OP meets the line y = 1, on the extension of the ray beyond O (dashed).

All four functions of 234°
FunctionExact valueDecimal
sin 234°−(√5 + 1)/4≈ −0.8090
cos 234°−√(10 − 2√5)/4≈ −0.5878
tan 234°√(25 + 10√5)/5≈ 1.3764
cot 234°√(5 − 2√5)≈ 0.7265

Reference angle: cot 54° = √(5 − 2√5)

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
216°√(25 + 10√5)/5
225°1
227°≈ 0.9325
234°√(5 − 2√5)
240°√3/3
252°√(25 − 10√5)/5
255°2 − √3

FAQ

What is cot 234°?

cot 234° = √(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 0.0487 for cot 234?

The calculator is in radian mode (RAD): it takes cot 234 as the cotangent of 234 radians, cot 234 rad ≈ 0.0487. Switch it to degrees (DEG): cot 234° = √(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