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    Cos 225 Degrees

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

    What is cos 225°?

    Answer

    cos 225° =
    −√2/2 ≈ −0.7071

    Angle in radians: 225° = 5π/4. The point of the angle is in quadrant III, where cosine is negative.

    ≈ — rounded to 4 decimal places.

    cos 225° = cos(180° + 45°) = −cos 45° = −√2/2

    P(cos 225°, sin 225°) = (−√2/2, −√2/2)

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

    cos 45° = 1/√2 = √2/2

    xyOP

    P(cos 225°, sin 225°) ≈ (−0.7071, −0.7071)

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

    All four functions of 225°
    FunctionExact valueDecimal
    sin 225°−√2/2≈ −0.7071
    cos 225°−√2/2≈ −0.7071
    tan 225°11
    cot 225°11

    Reference angle: cos 45° = √2/2

    See Also

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    https://calculat.io/en/number/trigonometry/cos--225Copy
    <a href="https://calculat.io/en/number/trigonometry/cos--225">Cos 225 Degrees: Cosine of 225° on the Unit Circle</a>Copy
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    Cos 225 Degrees: Cosine of 225° on the Unit Circle. cos 225° = −√2/2 ≈ −0.7071. The cosine is the x-coordinate of the point at 225° on the unit circle; 225° reduces to 45°.
    https://calculat.io/en/number/trigonometry/cos--225/generated.jpgCopy

    Cosine of nearby angles

    Anglecos
    211°≈ −0.8572
    215°≈ −0.8192
    216°−(√5 + 1)/4
    225°−√2/2
    227°≈ −0.6820
    234°−√(10 − 2√5)/4
    240°−1/2
    Recalculate with different values ↑

    FAQ

    What is cos 225°?

    cos 225° = −√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 225° = −√2/2 ≈ −0.7071.

    Why does a calculator show 0.3673 for cos 225?

    The calculator is in radian mode (RAD): it takes cos 225 as the cosine of 225 radians, cos 225 rad ≈ 0.3673. Switch it to degrees (DEG): cos 225° = −√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