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    Sin 198 Degrees

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

    What is sin 198°?

    Answer

    sin 198° =
    −(√5 − 1)/4 ≈ −0.3090

    Angle in radians: 198° = 11π/10. The point of the angle is in quadrant III, where sine is negative.

    ≈ — rounded to 4 decimal places.

    sin 198° = sin(180° + 18°) = −sin 18° = −(√5 − 1)/4

    P(cos 198°, sin 198°) = (−√(10 + 2√5)/4, −(√5 − 1)/4)

    Regular pentagon (golden ratio): cos 36° = (√5 + 1)/4.

    sin 18° = cos 72° = 2 cos² 36° − 1 = (√5 − 1)/4

    xyOP

    P(cos 198°, sin 198°) ≈ (−0.9511, −0.3090)

    Highlighted: the projection on the y-axis — sine, y ≈ −0.3090.

    All four functions of 198°
    FunctionExact valueDecimal
    sin 198°−(√5 − 1)/4≈ −0.3090
    cos 198°−√(10 + 2√5)/4≈ −0.9511
    tan 198°√(25 − 10√5)/5≈ 0.3249
    cot 198°√(5 + 2√5)≈ 3.0777

    Reference angle: sin 18° = (√5 − 1)/4

    See Also

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    https://calculat.io/en/number/trigonometry/sin--198Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--198">Sin 198 Degrees: Sine of 198° on the Unit Circle</a>Copy
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    Sin 198 Degrees: Sine of 198° on the Unit Circle. sin 198° = −(√5 − 1)/4 ≈ −0.3090. The sine is the y-coordinate of the point at 198° on the unit circle; 198° reduces to 18°.
    https://calculat.io/en/number/trigonometry/sin--198/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    179°≈ 0.0175
    180°0
    195°−(√6 − √2)/4
    198°−(√5 − 1)/4
    200°≈ −0.3420
    210°−1/2
    211°≈ −0.5150
    Recalculate with different values ↑

    FAQ

    What is sin 198°?

    sin 198° = −(√5 − 1)/4 ≈ −0.3090

    How are sin 18° and cos 72° related?

    They are equal: sin α = cos(90° − α), and 18° + 72° = 90°. So sin 18° = cos 72° = (√5 − 1)/4, cos 18° = sin 72° = √(10 + 2√5)/4, and tan 18° = cot 72° = √(25 − 10√5)/5.

    Why does a calculator show −0.0796 for sin 198?

    The calculator is in radian mode (RAD): it takes sin 198 as the sine of 198 radians, sin 198 rad ≈ −0.0796. Switch it to degrees (DEG): sin 198° = −(√5 − 1)/4 ≈ −0.3090. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also