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    Tan 135 Degrees

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

    What is tan 135°?

    Answer

    tan 135° =
    −1

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

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

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

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

    tan 45° = 1/1 = 1

    xyOP

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

    T(1, tan 135°) = (1, −1) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

    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: tan 45° = 1

    See Also

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

    Tangent of nearby angles

    Angletan
    127°≈ −1.3270
    130°≈ −1.1918
    134°≈ −1.0355
    135°−1
    140°≈ −0.8391
    142°≈ −0.7813
    144°−√(5 − 2√5)
    Recalculate with different values ↑

    FAQ

    What is tan 135°?

    tan 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: tan 135° = −1.

    Why does a calculator show −0.0887 for tan 135?

    The calculator is in radian mode (RAD): it takes tan 135 as the tangent of 135 radians, tan 135 rad ≈ −0.0887. Switch it to degrees (DEG): tan 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