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    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

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    https://calculat.io/en/number/trigonometry/cot--135Copy
    <a href="https://calculat.io/en/number/trigonometry/cot--135">Cot 135 Degrees: Cotangent of 135° on the Unit Circle</a>Copy
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    Cot 135 Degrees: Cotangent of 135° on the Unit Circle. cot 135° = −1. The cotangent is the ratio x/y of the point at 135° on the unit circle; 135° reduces to 45°.
    https://calculat.io/en/number/trigonometry/cot--135/generated.jpgCopy

    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
    Recalculate with different values ↑

    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