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    Cos 315 Degrees

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

    What is cos 315°?

    Answer

    cos 315° =
    √2/2 ≈ 0.7071

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

    ≈ — rounded to 4 decimal places.

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

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

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

    cos 45° = 1/√2 = √2/2

    xyOP

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

    Highlighted: the projection on the x-axis — cosine, x ≈ 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: cos 45° = √2/2

    See Also

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    https://calculat.io/en/number/trigonometry/cos--315Copy
    <a href="https://calculat.io/en/number/trigonometry/cos--315">Cos 315 Degrees: Cosine of 315° on the Unit Circle</a>Copy
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    Cos 315 Degrees: Cosine of 315° on the Unit Circle. cos 315° = √2/2 ≈ 0.7071. The cosine is the x-coordinate of the point at 315° on the unit circle; 315° reduces to 45°.
    https://calculat.io/en/number/trigonometry/cos--315/generated.jpgCopy

    Cosine of nearby angles

    Anglecos
    288°(√5 − 1)/4
    300°1/2
    306°√(10 − 2√5)/4
    315°√2/2
    324°(√5 + 1)/4
    330°√3/2
    341°≈ 0.9455
    Recalculate with different values ↑

    FAQ

    What is cos 315°?

    cos 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: cos 315° = √2/2 ≈ 0.7071.

    Why does a calculator show 0.6669 for cos 315?

    The calculator is in radian mode (RAD): it takes cos 315 as the cosine of 315 radians, cos 315 rad ≈ 0.6669. Switch it to degrees (DEG): cos 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