Cot 126 Degrees

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

What is cot 126°?

Answer

cot 126° =
−√(5 − 2√5) ≈ −0.7265

Angle in radians: 126° = 7π/10. The point of the angle is in quadrant II, where cotangent is negative.

≈ — rounded to 4 decimal places.

cot 126° = cot(180° − 54°) = −cot 54° = −√(5 − 2√5)

cot 126° = cos 126° / sin 126° = (−√(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 126°, sin 126°) ≈ (−0.5878, 0.8090)

C(cot 126°, 1) ≈ (−0.7265, 1) — where line OP meets the line y = 1.

All four functions of 126°
FunctionExact valueDecimal
sin 126°(√5 + 1)/4≈ 0.8090
cos 126°−√(10 − 2√5)/4≈ −0.5878
tan 126°−√(25 + 10√5)/5≈ −1.3764
cot 126°−√(5 − 2√5)≈ −0.7265

Reference angle: cot 54° = √(5 − 2√5)

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
110°≈ −0.3640
120°−√3/3
125°≈ −0.7002
126°−√(5 − 2√5)
127°≈ −0.7536
130°≈ −0.8391
134°≈ −0.9657

FAQ

What is cot 126°?

cot 126° = −√(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 2.8606 for cot 126?

The calculator is in radian mode (RAD): it takes cot 126 as the cotangent of 126 radians, cot 126 rad ≈ 2.8606. Switch it to degrees (DEG): cot 126° = −√(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