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    Sin 195 Degrees

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

    What is sin 195°?

    Answer

    sin 195° =
    −(√6 − √2)/4 ≈ −0.2588

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

    ≈ — rounded to 4 decimal places.

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

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

    sin 15° = sin(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 y-axis — sine, y ≈ −0.2588.

    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: sin 15° = (√6 − √2)/4

    See Also

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    https://calculat.io/en/number/trigonometry/sin--195Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--195">Sin 195 Degrees: Sine of 195° on the Unit Circle</a>Copy
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    Sin 195 Degrees: Sine of 195° on the Unit Circle. sin 195° = −(√6 − √2)/4 ≈ −0.2588. The sine is the y-coordinate of the point at 195° on the unit circle; 195° reduces to 15°.
    https://calculat.io/en/number/trigonometry/sin--195/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    175°≈ 0.0872
    179°≈ 0.0175
    180°0
    195°−(√6 − √2)/4
    198°−(√5 − 1)/4
    200°≈ −0.3420
    210°−1/2
    Recalculate with different values ↑

    FAQ

    What is sin 195°?

    sin 195° = −(√6 − √2)/4 ≈ −0.2588

    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 0.2195 for sin 195?

    The calculator is in radian mode (RAD): it takes sin 195 as the sine of 195 radians, sin 195 rad ≈ 0.2195. Switch it to degrees (DEG): sin 195° = −(√6 − √2)/4 ≈ −0.2588. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also