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    Cot 162 Degrees

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

    What is cot 162°?

    Answer

    cot 162° =
    −√(5 + 2√5) ≈ −3.0777

    Angle in radians: 162° = 9π/10. The point of the angle is in quadrant II, where cotangent is negative.

    ≈ — rounded to 4 decimal places.

    cot 162° = cot(180° − 18°) = −cot 18° = −√(5 + 2√5)

    cot 162° = cos 162° / sin 162° = (−√(10 + 2√5)/4) / ((√5 − 1)/4) = −√(5 + 2√5)

    Regular pentagon (golden ratio): cos 36° = (√5 + 1)/4.

    cot 18° = cos 18° / sin 18° = √(5 + 2√5)

    xyOP

    P(cos 162°, sin 162°) ≈ (−0.9511, 0.3090)

    C(cot 162°, 1) ≈ (−3.0777, 1) — where line OP meets the line y = 1; C is beyond the drawing, the arrow points to it.

    All four functions of 162°
    FunctionExact valueDecimal
    sin 162°(√5 − 1)/4≈ 0.3090
    cos 162°−√(10 + 2√5)/4≈ −0.9511
    tan 162°−√(25 − 10√5)/5≈ −0.3249
    cot 162°−√(5 + 2√5)≈ −3.0777

    Reference angle: cot 18° = √(5 + 2√5)

    See Also

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    https://calculat.io/en/number/trigonometry/cot--162Copy
    <a href="https://calculat.io/en/number/trigonometry/cot--162">Cot 162 Degrees: Cotangent of 162° on the Unit Circle</a>Copy
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    Cot 162 Degrees: Cotangent of 162° on the Unit Circle. cot 162° = −√(5 + 2√5) ≈ −3.0777. The cotangent is the ratio x/y of the point at 162° on the unit circle; 162° reduces to 18°.
    https://calculat.io/en/number/trigonometry/cot--162/generated.jpgCopy

    Cotangent of nearby angles

    Anglecot
    150°−√3
    159°≈ −2.6051
    160°≈ −2.7475
    162°−√(5 + 2√5)
    164°≈ −3.4874
    165°−2 − √3
    167°≈ −4.3315
    Recalculate with different values ↑

    FAQ

    What is cot 162°?

    cot 162° = −√(5 + 2√5) ≈ −3.0777

    How are sin 18° and cos 72° related?

    They are equal: sin α = cos(90° − α), and 18° + 72° = 90°. So sin 18° = cos 72° = (√5 − 1)/4, cos 18° = sin 72° = √(10 + 2√5)/4, and tan 18° = cot 72° = √(25 − 10√5)/5.

    Why does a calculator show −0.2110 for cot 162?

    The calculator is in radian mode (RAD): it takes cot 162 as the cotangent of 162 radians, cot 162 rad ≈ −0.2110. Switch it to degrees (DEG): cot 162° = −√(5 + 2√5) ≈ −3.0777. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also