Cot 285 Degrees

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

What is cot 285°?

Answer

cot 285° =
√3 − 2 ≈ −0.2679

Angle in radians: 285° = 19π/12. The point of the angle is in quadrant IV, where cotangent is negative.

≈ — rounded to 4 decimal places.

cot 285° = cot(360° − 75°) = −cot 75° = √3 − 2

cot 285° = cos 285° / sin 285° = ((√6 − √2)/4) / (−(√6 + √2)/4) = √3 − 2

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

xyOP

P(cos 285°, sin 285°) ≈ (0.2588, −0.9659)

C(cot 285°, 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 285°
FunctionExact valueDecimal
sin 285°−(√6 + √2)/4≈ −0.9659
cos 285°(√6 − √2)/4≈ 0.2588
tan 285°−2 − √3≈ −3.7321
cot 285°√3 − 2≈ −0.2679

Reference angle: cot 75° = 2 − √3

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
252°√(25 − 10√5)/5
255°2 − √3
270°0
285°√3 − 2
288°−√(25 − 10√5)/5
300°−√3/3
306°−√(5 − 2√5)

FAQ

What is cot 285°?

cot 285° = √3 − 2 ≈ −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 −0.8184 for cot 285?

The calculator is in radian mode (RAD): it takes cot 285 as the cotangent of 285 radians, cot 285 rad ≈ −0.8184. Switch it to degrees (DEG): cot 285° = √3 − 2 ≈ −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