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    Sin 75 Degrees

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

    What is sin 75°?

    Answer

    sin 75° =
    (√6 + √2)/4 ≈ 0.9659

    Angle in radians: 75° = 5π/12. The point of the angle is in quadrant I, where sine is positive.

    ≈ — rounded to 4 decimal places.

    P(cos 75°, sin 75°) = ((√6 − √2)/4, (√6 + √2)/4)

    sin 75° = sin(45° + 30°) = (√2/2)(√3/2) + (√2/2)(1/2) = (√6 + √2)/4

    xyOP

    P(cos 75°, sin 75°) ≈ (0.2588, 0.9659)

    Highlighted: the projection on the y-axis — sine, y ≈ 0.9659.

    All four functions of 75°
    FunctionExact valueDecimal
    sin 75°(√6 + √2)/4≈ 0.9659
    cos 75°(√6 − √2)/4≈ 0.2588
    tan 75°2 + √3≈ 3.7321
    cot 75°2 − √3≈ 0.2679

    See Also

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    https://calculat.io/en/number/trigonometry/sin--75Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--75">Sin 75 Degrees: Sine of 75° on the Unit Circle - Calculatio</a>Copy
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    Sin 75 Degrees: Sine of 75° on the Unit Circle. sin 75° = (√6 + √2)/4 ≈ 0.9659. The sine is the y-coordinate of the point at 75° on the unit circle.
    https://calculat.io/en/number/trigonometry/sin--75/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    72°√(10 + 2√5)/4
    73°≈ 0.9563
    74°≈ 0.9613
    75°(√6 + √2)/4
    76°≈ 0.9703
    77°≈ 0.9744
    78°≈ 0.9781
    Recalculate with different values ↑

    FAQ

    What is sin 75°?

    sin 75° = (√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 −0.3878 for sin 75?

    The calculator is in radian mode (RAD): it takes sin 75 as the sine of 75 radians, sin 75 rad ≈ −0.3878. Switch it to degrees (DEG): sin 75° = (√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