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    Tan 225 Degrees

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

    What is tan 225°?

    Answer

    tan 225° =
    1

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

    tan 225° = tan(180° + 45°) = tan 45° = 1

    tan 225° = sin 225° / cos 225° = (−√2/2) / (−√2/2) = 1

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

    tan 45° = 1/1 = 1

    xyOP

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

    T(1, tan 225°) = (1, 1) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

    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: tan 45° = 1

    See Also

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    https://calculat.io/en/number/trigonometry/tan--225Copy
    <a href="https://calculat.io/en/number/trigonometry/tan--225">Tan 225 Degrees: Tangent of 225° on the Unit Circle</a>Copy
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    Tan 225 Degrees: Tangent of 225° on the Unit Circle. tan 225° = 1. The tangent is the ratio y/x of the point at 225° on the unit circle; 225° reduces to 45°.
    https://calculat.io/en/number/trigonometry/tan--225/generated.jpgCopy

    Tangent of nearby angles

    Angletan
    211°≈ 0.6009
    215°≈ 0.7002
    216°√(5 − 2√5)
    225°1
    227°≈ 1.0724
    234°√(25 + 10√5)/5
    240°√3
    Recalculate with different values ↑

    FAQ

    What is tan 225°?

    tan 225° = 1

    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: tan 225° = 1.

    Why does a calculator show −2.5321 for tan 225?

    The calculator is in radian mode (RAD): it takes tan 225 as the tangent of 225 radians, tan 225 rad ≈ −2.5321. Switch it to degrees (DEG): tan 225° = 1. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also