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    Cos 135 Degrees

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

    What is cos 135°?

    Answer

    cos 135° =
    −√2/2 ≈ −0.7071

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

    ≈ — rounded to 4 decimal places.

    cos 135° = cos(180° − 45°) = −cos 45° = −√2/2

    P(cos 135°, sin 135°) = (−√2/2, √2/2)

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

    cos 45° = 1/√2 = √2/2

    xyOP

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

    Highlighted: the projection on the x-axis — cosine, x ≈ −0.7071.

    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: cos 45° = √2/2

    See Also

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    https://calculat.io/en/number/trigonometry/cos--135Copy
    <a href="https://calculat.io/en/number/trigonometry/cos--135">Cos 135 Degrees: Cosine of 135° on the Unit Circle</a>Copy
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    Cos 135 Degrees: Cosine of 135° on the Unit Circle. cos 135° = −√2/2 ≈ −0.7071. The cosine is the x-coordinate of the point at 135° on the unit circle; 135° reduces to 45°.
    https://calculat.io/en/number/trigonometry/cos--135/generated.jpgCopy

    Cosine of nearby angles

    Anglecos
    127°≈ −0.6018
    130°≈ −0.6428
    134°≈ −0.6947
    135°−√2/2
    140°≈ −0.7660
    142°≈ −0.7880
    144°−(√5 + 1)/4
    Recalculate with different values ↑

    FAQ

    What is cos 135°?

    cos 135° = −√2/2 ≈ −0.7071

    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: cos 135° = −√2/2 ≈ −0.7071.

    Why does a calculator show −0.9961 for cos 135?

    The calculator is in radian mode (RAD): it takes cos 135 as the cosine of 135 radians, cos 135 rad ≈ −0.9961. Switch it to degrees (DEG): cos 135° = −√2/2 ≈ −0.7071. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also