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    Cos 195 Degrees

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

    What is cos 195°?

    Answer

    cos 195° =
    −(√6 + √2)/4 ≈ −0.9659

    Angle in radians: 195° = 13π/12. The point of the angle is in quadrant III, where cosine is negative.

    ≈ — rounded to 4 decimal places.

    cos 195° = cos(180° + 15°) = −cos 15° = −(√6 + √2)/4

    P(cos 195°, sin 195°) = (−(√6 + √2)/4, −(√6 − √2)/4)

    cos 15° = cos(45° − 30°) = (√2/2)(√3/2) + (√2/2)(1/2) = (√6 + √2)/4

    xyOP

    P(cos 195°, sin 195°) ≈ (−0.9659, −0.2588)

    Highlighted: the projection on the x-axis — cosine, x ≈ −0.9659.

    All four functions of 195°
    FunctionExact valueDecimal
    sin 195°−(√6 − √2)/4≈ −0.2588
    cos 195°−(√6 + √2)/4≈ −0.9659
    tan 195°2 − √3≈ 0.2679
    cot 195°2 + √3≈ 3.7321

    Reference angle: cos 15° = (√6 + √2)/4

    See Also

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    https://calculat.io/en/number/trigonometry/cos--195Copy
    <a href="https://calculat.io/en/number/trigonometry/cos--195">Cos 195 Degrees: Cosine of 195° on the Unit Circle</a>Copy
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    Cos 195 Degrees: Cosine of 195° on the Unit Circle. cos 195° = −(√6 + √2)/4 ≈ −0.9659. The cosine is the x-coordinate of the point at 195° on the unit circle; 195° reduces to 15°.
    https://calculat.io/en/number/trigonometry/cos--195/generated.jpgCopy

    Cosine of nearby angles

    Anglecos
    175°≈ −0.9962
    179°≈ −0.9998
    180°−1
    195°−(√6 + √2)/4
    198°−√(10 + 2√5)/4
    200°≈ −0.9397
    210°−√3/2
    Recalculate with different values ↑

    FAQ

    What is cos 195°?

    cos 195° = −(√6 + √2)/4 ≈ −0.9659

    How are sin 15° and cos 75° related?

    They are equal: sin α = cos(90° − α), and 15° + 75° = 90°. So sin 15° = cos 75° = (√6 − √2)/4, cos 15° = sin 75° = (√6 + √2)/4, and tan 15° = cot 75° = 2 − √3.

    Why does a calculator show 0.9756 for cos 195?

    The calculator is in radian mode (RAD): it takes cos 195 as the cosine of 195 radians, cos 195 rad ≈ 0.9756. Switch it to degrees (DEG): cos 195° = −(√6 + √2)/4 ≈ −0.9659. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also