Cot 255 Degrees

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

What is cot 255°?

Answer

cot 255° =
2 − √3 ≈ 0.2679

Angle in radians: 255° = 17π/12. The point of the angle is in quadrant III, where cotangent is positive.

≈ — rounded to 4 decimal places.

cot 255° = cot(180° + 75°) = cot 75° = 2 − √3

cot 255° = cos 255° / sin 255° = (−(√6 − √2)/4) / (−(√6 + √2)/4) = 2 − √3

cot 75° = 1 / tan 75° = 1 / (2 + √3) = 2 − √3

xyOP

P(cos 255°, sin 255°) ≈ (−0.2588, −0.9659)

C(cot 255°, 1) ≈ (0.2679, 1) — where line OP meets the line y = 1, on the extension of the ray beyond O (dashed).

All four functions of 255°
FunctionExact valueDecimal
sin 255°−(√6 + √2)/4≈ −0.9659
cos 255°−(√6 − √2)/4≈ −0.2588
tan 255°2 + √3≈ 3.7321
cot 255°2 − √3≈ 0.2679

Reference angle: cot 75° = 2 − √3

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
234°√(5 − 2√5)
240°√3/3
252°√(25 − 10√5)/5
255°2 − √3
270°0
285°√3 − 2
288°−√(25 − 10√5)/5

FAQ

What is cot 255°?

cot 255° = 2 − √3 ≈ 0.2679

How are sin 15° and cos 75° related?

They are equal: sin α = cos(90° − α), and 15° + 75° = 90°. So sin 15° = cos 75° = (√6 − √2)/4, cos 15° = sin 75° = (√6 + √2)/4, and tan 15° = cot 75° = 2 − √3.

Why does a calculator show 1.7028 for cot 255?

The calculator is in radian mode (RAD): it takes cot 255 as the cotangent of 255 radians, cot 255 rad ≈ 1.7028. Switch it to degrees (DEG): cot 255° = 2 − √3 ≈ 0.2679. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also