Cot 306 Degrees

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

What is cot 306°?

Answer

cot 306° =
−√(5 − 2√5) ≈ −0.7265

Angle in radians: 306° = 17π/10. The point of the angle is in quadrant IV, where cotangent is negative.

≈ — rounded to 4 decimal places.

cot 306° = cot(360° − 54°) = −cot 54° = −√(5 − 2√5)

cot 306° = cos 306° / sin 306° = (√(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 306°, sin 306°) ≈ (0.5878, −0.8090)

C(cot 306°, 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 306°
FunctionExact valueDecimal
sin 306°−(√5 + 1)/4≈ −0.8090
cos 306°√(10 − 2√5)/4≈ 0.5878
tan 306°−√(25 + 10√5)/5≈ −1.3764
cot 306°−√(5 − 2√5)≈ −0.7265

Reference angle: cot 54° = √(5 − 2√5)

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
285°√3 − 2
288°−√(25 − 10√5)/5
300°−√3/3
306°−√(5 − 2√5)
315°−1
324°−√(25 + 10√5)/5
330°−√3

FAQ

What is cot 306°?

cot 306° = −√(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 0.3151 for cot 306?

The calculator is in radian mode (RAD): it takes cot 306 as the cotangent of 306 radians, cot 306 rad ≈ 0.3151. Switch it to degrees (DEG): cot 306° = −√(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