Cot 330 Degrees

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

What is cot 330°?

Answer

cot 330° =
−√3 ≈ −1.7321

Angle in radians: 330° = 11π/6. The point of the angle is in quadrant IV, where cotangent is negative.

≈ — rounded to 4 decimal places.

cot 330° = cot(360° − 30°) = −cot 30° = −√3

cot 330° = cos 330° / sin 330° = (√3/2) / (−1/2) = −√3

Half of an equilateral triangle with side 1: the hypotenuse is 1 and the leg opposite 30° is 1/2.

cot 30° = (√3/2) / (1/2) = √3

xyOP

P(cos 330°, sin 330°) ≈ (0.8660, −0.5)

C(cot 330°, 1) ≈ (−1.7321, 1) — where line OP meets the line y = 1, on the extension of the ray beyond O (dashed).

All four functions of 330°
FunctionExact valueDecimal
sin 330°−1/2−0.5
cos 330°√3/2≈ 0.8660
tan 330°−√3/3≈ −0.5774
cot 330°−√3≈ −1.7321

Reference angle: cot 30° = √3

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
306°−√(5 − 2√5)
315°−1
324°−√(25 + 10√5)/5
330°−√3
341°≈ −2.9042
342°−√(5 + 2√5)
345°−2 − √3

FAQ

What is cot 330°?

cot 330° = −√3 ≈ −1.7321

How to remember sin 30°, sin 45° and sin 60°?

Write them as √1/2, √2/2, √3/2: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2. Cosines are the same numbers in reverse order: cos 30° = √3/2, cos 45° = √2/2, cos 60° = 1/2; tan = sin / cos and cot = cos / sin. Here: cot 330° = −√3 ≈ −1.7321.

Why does a calculator show 7.4874 for cot 330?

The calculator is in radian mode (RAD): it takes cot 330 as the cotangent of 330 radians, cot 330 rad ≈ 7.4874. Switch it to degrees (DEG): cot 330° = −√3 ≈ −1.7321. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also