Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    Sin 315 Degrees

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

    What is sin 315°?

    Answer

    sin 315° =
    −√2/2 ≈ −0.7071

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

    ≈ — rounded to 4 decimal places.

    sin 315° = sin(360° − 45°) = −sin 45° = −√2/2

    P(cos 315°, sin 315°) = (√2/2, −√2/2)

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

    sin 45° = 1/√2 = √2/2

    xyOP

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

    Highlighted: the projection on the y-axis — sine, y ≈ −0.7071.

    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: sin 45° = √2/2

    See Also

    Share This Calculation
    Print
    https://calculat.io/en/number/trigonometry/sin--315Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--315">Sin 315 Degrees: Sine of 315° on the Unit Circle</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    Sin 315 Degrees: Sine of 315° on the Unit Circle. sin 315° = −√2/2 ≈ −0.7071. The sine is the y-coordinate of the point at 315° on the unit circle; 315° reduces to 45°.
    https://calculat.io/en/number/trigonometry/sin--315/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    288°−√(10 + 2√5)/4
    300°−√3/2
    306°−(√5 + 1)/4
    315°−√2/2
    324°−√(10 − 2√5)/4
    330°−1/2
    341°≈ −0.3256
    Recalculate with different values ↑

    FAQ

    What is sin 315°?

    sin 315° = −√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 315° = −√2/2 ≈ −0.7071.

    Why does a calculator show 0.7451 for sin 315?

    The calculator is in radian mode (RAD): it takes sin 315 as the sine of 315 radians, sin 315 rad ≈ 0.7451. Switch it to degrees (DEG): sin 315° = −√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