Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    Sin 135 Degrees

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

    What is sin 135°?

    Answer

    sin 135° =
    √2/2 ≈ 0.7071

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

    ≈ — rounded to 4 decimal places.

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

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

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

    sin 45° = 1/√2 = √2/2

    xyOP

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

    Highlighted: the projection on the y-axis — sine, y ≈ 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: sin 45° = √2/2

    See Also

    Share This Calculation
    Print
    https://calculat.io/en/number/trigonometry/sin--135Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--135">Sin 135 Degrees: Sine of 135° on the Unit Circle</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    Sin 135 Degrees: Sine of 135° on the Unit Circle. sin 135° = √2/2 ≈ 0.7071. The sine is the y-coordinate of the point at 135° on the unit circle; 135° reduces to 45°.
    https://calculat.io/en/number/trigonometry/sin--135/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    127°≈ 0.7986
    130°≈ 0.7660
    134°≈ 0.7193
    135°√2/2
    140°≈ 0.6428
    142°≈ 0.6157
    144°√(10 − 2√5)/4
    Recalculate with different values ↑

    FAQ

    What is sin 135°?

    sin 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: sin 135° = √2/2 ≈ 0.7071.

    Why does a calculator show 0.0884 for sin 135?

    The calculator is in radian mode (RAD): it takes sin 135 as the sine of 135 radians, sin 135 rad ≈ 0.0884. Switch it to degrees (DEG): sin 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