Cot 252 Degrees

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

What is cot 252°?

Answer

cot 252° =
√(25 − 10√5)/5 ≈ 0.3249

Angle in radians: 252° = 7π/5. The point of the angle is in quadrant III, where cotangent is positive.

≈ — rounded to 4 decimal places.

cot 252° = cot(180° + 72°) = cot 72° = √(25 − 10√5)/5

cot 252° = cos 252° / sin 252° = (−(√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 252°, sin 252°) ≈ (−0.3090, −0.9511)

C(cot 252°, 1) ≈ (0.3249, 1) — where line OP meets the line y = 1, on the extension of the ray beyond O (dashed).

All four functions of 252°
FunctionExact valueDecimal
sin 252°−√(10 + 2√5)/4≈ −0.9511
cos 252°−(√5 − 1)/4≈ −0.3090
tan 252°√(5 + 2√5)≈ 3.0777
cot 252°√(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
227°≈ 0.9325
234°√(5 − 2√5)
240°√3/3
252°√(25 − 10√5)/5
255°2 − √3
270°0
285°√3 − 2

FAQ

What is cot 252°?

cot 252° = √(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 1.2555 for cot 252?

The calculator is in radian mode (RAD): it takes cot 252 as the cotangent of 252 radians, cot 252 rad ≈ 1.2555. Switch it to degrees (DEG): cot 252° = √(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