Cot 300 Degrees

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

What is cot 300°?

Answer

cot 300° =
−√3/3 ≈ −0.5774

Angle in radians: 300° = 5π/3. The point of the angle is in quadrant IV, where cotangent is negative.

≈ — rounded to 4 decimal places.

cot 300° = cot(360° − 60°) = −cot 60° = −√3/3

cot 300° = cos 300° / sin 300° = (1/2) / (−√3/2) = −√3/3

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

cot 60° = (1/2) / (√3/2) = 1/√3 = √3/3

xyOP

P(cos 300°, sin 300°) ≈ (0.5, −0.8660)

C(cot 300°, 1) ≈ (−0.5774, 1) — where line OP meets the line y = 1, on the extension of the ray beyond O (dashed).

All four functions of 300°
FunctionExact valueDecimal
sin 300°−√3/2≈ −0.8660
cos 300°1/20.5
tan 300°−√3≈ −1.7321
cot 300°−√3/3≈ −0.5774

Reference angle: cot 60° = √3/3

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
270°0
285°√3 − 2
288°−√(25 − 10√5)/5
300°−√3/3
306°−√(5 − 2√5)
315°−1
324°−√(25 + 10√5)/5

FAQ

What is cot 300°?

cot 300° = −√3/3 ≈ −0.5774

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 300° = −√3/3 ≈ −0.5774.

Why does a calculator show 0.0221 for cot 300?

The calculator is in radian mode (RAD): it takes cot 300 as the cotangent of 300 radians, cot 300 rad ≈ 0.0221. Switch it to degrees (DEG): cot 300° = −√3/3 ≈ −0.5774. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also