Cot 690 Degrees

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

What is cot 690°?

Answer

cot 690° =
−√3 ≈ −1.7321

Angle in radians: 690° = 23π/6. 690° = 360° + 330° — a full turn plus 330°, quadrant IV, where cotangent is negative.

≈ — rounded to 4 decimal places.

cot 690° = cot(690° − 360°) = cot 330°

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

cot 690° = cos 690° / sin 690° = (√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 690°, sin 690°) ≈ (0.8660, −0.5)

C(cot 690°, 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 330°.

All four functions of 690°
FunctionExact valueDecimal
sin 690°−1/2−0.5
cos 690°√3/2≈ 0.8660
tan 690°−√3/3≈ −0.5774
cot 690°−√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 690°?

cot 690° = −√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 690° = −√3 ≈ −1.7321.

Why does a calculator show −0.4471 for cot 690?

The calculator is in radian mode (RAD): it takes cot 690 as the cotangent of 690 radians, cot 690 rad ≈ −0.4471. Switch it to degrees (DEG): cot 690° = −√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