Cot 105 Degrees

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

What is cot 105°?

Answer

cot 105° =
√3 − 2 ≈ −0.2679

Angle in radians: 105° = 7π/12. The point of the angle is in quadrant II, where cotangent is negative.

≈ — rounded to 4 decimal places.

cot 105° = cot(180° − 75°) = −cot 75° = √3 − 2

cot 105° = cos 105° / sin 105° = (−(√6 − √2)/4) / ((√6 + √2)/4) = √3 − 2

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

xyOP

P(cos 105°, sin 105°) ≈ (−0.2588, 0.9659)

C(cot 105°, 1) ≈ (−0.2679, 1) — where line OP meets the line y = 1.

All four functions of 105°
FunctionExact valueDecimal
sin 105°(√6 + √2)/4≈ 0.9659
cos 105°−(√6 − √2)/4≈ −0.2588
tan 105°−2 − √3≈ −3.7321
cot 105°√3 − 2≈ −0.2679

Reference angle: cot 75° = 2 − √3

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
98°≈ −0.1405
100°≈ −0.1763
101°≈ −0.1944
105°√3 − 2
106°≈ −0.2867
108°−√(25 − 10√5)/5
110°≈ −0.3640

FAQ

What is cot 105°?

cot 105° = √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 0.2483 for cot 105?

The calculator is in radian mode (RAD): it takes cot 105 as the cotangent of 105 radians, cot 105 rad ≈ 0.2483. Switch it to degrees (DEG): cot 105° = √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