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    Tan 315 Degrees

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

    What is tan 315°?

    Answer

    tan 315° =
    −1

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

    tan 315° = tan(360° − 45°) = −tan 45° = −1

    tan 315° = sin 315° / cos 315° = (−√2/2) / (√2/2) = −1

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

    tan 45° = 1/1 = 1

    xyOP

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

    T(1, tan 315°) = (1, −1) — where line OP meets the line x = 1.

    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: tan 45° = 1

    See Also

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    https://calculat.io/en/number/trigonometry/tan--315Copy
    <a href="https://calculat.io/en/number/trigonometry/tan--315">Tan 315 Degrees: Tangent of 315° on the Unit Circle</a>Copy
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    Tan 315 Degrees: Tangent of 315° on the Unit Circle. tan 315° = −1. The tangent is the ratio y/x of the point at 315° on the unit circle; 315° reduces to 45°.
    https://calculat.io/en/number/trigonometry/tan--315/generated.jpgCopy

    Tangent of nearby angles

    Angletan
    288°−√(5 + 2√5)
    300°−√3
    306°−√(25 + 10√5)/5
    315°−1
    324°−√(5 − 2√5)
    330°−√3/3
    341°≈ −0.3443
    Recalculate with different values ↑

    FAQ

    What is tan 315°?

    tan 315° = −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 315° = −1.

    Why does a calculator show 1.1173 for tan 315?

    The calculator is in radian mode (RAD): it takes tan 315 as the tangent of 315 radians, tan 315 rad ≈ 1.1173. Switch it to degrees (DEG): tan 315° = −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