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    Cot 315 Degrees

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

    What is cot 315°?

    Answer

    cot 315° =
    −1

    Angle in radians: 315° = 7π/4. The point of the angle is in quadrant IV, where cotangent is negative.

    cot 315° = cot(360° − 45°) = −cot 45° = −1

    cot 315° = cos 315° / sin 315° = (√2/2) / (−√2/2) = −1

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

    cot 45° = 1/1 = 1

    xyOP

    P(cos 315°, sin 315°) ≈ (0.7071, −0.7071)

    C(cot 315°, 1) = (−1, 1) — where line OP meets the line y = 1, on the extension of the ray beyond O (dashed).

    All four functions of 315°
    FunctionExact valueDecimal
    sin 315°−√2/2≈ −0.7071
    cos 315°√2/2≈ 0.7071
    tan 315°−1−1
    cot 315°−1−1

    Reference angle: cot 45° = 1

    See Also

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    https://calculat.io/en/number/trigonometry/cot--315Copy
    <a href="https://calculat.io/en/number/trigonometry/cot--315">Cot 315 Degrees: Cotangent of 315° on the Unit Circle</a>Copy
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    Cot 315 Degrees: Cotangent of 315° on the Unit Circle. cot 315° = −1. The cotangent is the ratio x/y of the point at 315° on the unit circle; 315° reduces to 45°.
    https://calculat.io/en/number/trigonometry/cot--315/generated.jpgCopy

    Cotangent of nearby angles

    Anglecot
    288°−√(25 − 10√5)/5
    300°−√3/3
    306°−√(5 − 2√5)
    315°−1
    324°−√(25 + 10√5)/5
    330°−√3
    341°≈ −2.9042
    Recalculate with different values ↑

    FAQ

    What is cot 315°?

    cot 315° = −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 315° = −1.

    Why does a calculator show 0.8950 for cot 315?

    The calculator is in radian mode (RAD): it takes cot 315 as the cotangent of 315 radians, cot 315 rad ≈ 0.8950. Switch it to degrees (DEG): cot 315° = −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