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    Sin 252 Degrees

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

    What is sin 252°?

    Answer

    sin 252° =
    −√(10 + 2√5)/4 ≈ −0.9511

    Angle in radians: 252° = 7π/5. The point of the angle is in quadrant III, where sine is negative.

    ≈ — rounded to 4 decimal places.

    sin 252° = sin(180° + 72°) = −sin 72° = −√(10 + 2√5)/4

    P(cos 252°, sin 252°) = (−(√5 − 1)/4, −√(10 + 2√5)/4)

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

    sin 72° = cos 18° = √(1 − sin² 18°) = √(10 + 2√5)/4

    xyOP

    P(cos 252°, sin 252°) ≈ (−0.3090, −0.9511)

    Highlighted: the projection on the y-axis — sine, y ≈ −0.9511.

    All four functions of 252°
    FunctionExact valueDecimal
    sin 252°−√(10 + 2√5)/4≈ −0.9511
    cos 252°−(√5 − 1)/4≈ −0.3090
    tan 252°√(5 + 2√5)≈ 3.0777
    cot 252°√(25 − 10√5)/5≈ 0.3249

    Reference angle: sin 72° = √(10 + 2√5)/4

    See Also

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    https://calculat.io/en/number/trigonometry/sin--252Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--252">Sin 252 Degrees: Sine of 252° on the Unit Circle</a>Copy
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    Sin 252 Degrees: Sine of 252° on the Unit Circle. sin 252° = −√(10 + 2√5)/4 ≈ −0.9511. The sine is the y-coordinate of the point at 252° on the unit circle; 252° reduces to 72°.
    https://calculat.io/en/number/trigonometry/sin--252/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    227°≈ −0.7314
    234°−(√5 + 1)/4
    240°−√3/2
    252°−√(10 + 2√5)/4
    255°−(√6 + √2)/4
    270°−1
    285°−(√6 + √2)/4
    Recalculate with different values ↑

    FAQ

    What is sin 252°?

    sin 252° = −√(10 + 2√5)/4 ≈ −0.9511

    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 0.6230 for sin 252?

    The calculator is in radian mode (RAD): it takes sin 252 as the sine of 252 radians, sin 252 rad ≈ 0.6230. Switch it to degrees (DEG): sin 252° = −√(10 + 2√5)/4 ≈ −0.9511. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also