Cot 75 Degrees

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

What is cot 75°?

Answer

cot 75° =
2 − √3 ≈ 0.2679

Angle in radians: 75° = 5π/12. The point of the angle is in quadrant I, where cotangent is positive.

≈ — rounded to 4 decimal places.

cot 75° = cos 75° / sin 75° = ((√6 − √2)/4) / ((√6 + √2)/4) = 2 − √3

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

xyOP

P(cos 75°, sin 75°) ≈ (0.2588, 0.9659)

C(cot 75°, 1) ≈ (0.2679, 1) — where line OP meets the line y = 1.

All four functions of 75°
FunctionExact valueDecimal
sin 75°(√6 + √2)/4≈ 0.9659
cos 75°(√6 − √2)/4≈ 0.2588
tan 75°2 + √3≈ 3.7321
cot 75°2 − √3≈ 0.2679

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
72°√(25 − 10√5)/5
73°≈ 0.3057
74°≈ 0.2867
75°2 − √3
76°≈ 0.2493
77°≈ 0.2309
78°≈ 0.2126

FAQ

What is cot 75°?

cot 75° = 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 −2.3770 for cot 75?

The calculator is in radian mode (RAD): it takes cot 75 as the cotangent of 75 radians, cot 75 rad ≈ −2.3770. Switch it to degrees (DEG): cot 75° = 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