Cot 135 Degrees

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

What is cot 135°?

Answer

cot 135° =
−1

Angle in radians: 135° = 3π/4. The point of the angle is in quadrant II, where cotangent is negative.

cot 135° = cot(180° − 45°) = −cot 45° = −1

cot 135° = cos 135° / sin 135° = (−√2/2) / (√2/2) = −1

An isosceles right triangle with legs 1: the hypotenuse is √2.

cot 45° = 1/1 = 1

xyOP

P(cos 135°, sin 135°) ≈ (−0.7071, 0.7071)

C(cot 135°, 1) = (−1, 1) — where line OP meets the line y = 1.

All four functions of 135°
FunctionExact valueDecimal
sin 135°√2/2≈ 0.7071
cos 135°−√2/2≈ −0.7071
tan 135°−1−1
cot 135°−1−1

Reference angle: cot 45° = 1

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
127°≈ −0.7536
130°≈ −0.8391
134°≈ −0.9657
135°−1
140°≈ −1.1918
142°≈ −1.2799
144°−√(25 + 10√5)/5

FAQ

What is cot 135°?

cot 135° = −1

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 135° = −1.

Why does a calculator show −11.2720 for cot 135?

The calculator is in radian mode (RAD): it takes cot 135 as the cotangent of 135 radians, cot 135 rad ≈ −11.2720. Switch it to degrees (DEG): cot 135° = −1. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also