Cot 570 Degrees

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

What is cot 570°?

Answer

cot 570° =
√3 ≈ 1.7321

Angle in radians: 570° = 19π/6. 570° = 360° + 210° — a full turn plus 210°, quadrant III, where cotangent is positive.

≈ — rounded to 4 decimal places.

cot 570° = cot(570° − 360°) = cot 210°

cot 210° = cot(180° + 30°) = cot 30° = √3

cot 570° = cos 570° / sin 570° = (−√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 570°, sin 570°) ≈ (−0.8660, −0.5)

C(cot 570°, 1) ≈ (1.7321, 1) — where line OP meets the line y = 1, on the extension of the ray beyond O (dashed).

+1 turn: the drawing shows 210°.

All four functions of 570°
FunctionExact valueDecimal
sin 570°−1/2−0.5
cos 570°−√3/2≈ −0.8660
tan 570°√3/3≈ 0.5774
cot 570°√3≈ 1.7321

Reference angle: cot 30° = √3

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
390°√3
400°≈ 1.1918
450°0
540°undefined
570°√3
690°−√3
720°undefined

FAQ

What is cot 570°?

cot 570° = √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 570° = √3 ≈ 1.7321.

Why does a calculator show 0.2017 for cot 570?

The calculator is in radian mode (RAD): it takes cot 570 as the cotangent of 570 radians, cot 570 rad ≈ 0.2017. Switch it to degrees (DEG): cot 570° = √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