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    Sin 45 Degrees

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

    What is sin 45°?

    Answer

    sin 45° =
    √2/2 ≈ 0.7071

    Angle in radians: 45° = π/4. The point of the angle is in quadrant I, where sine is positive.

    ≈ — rounded to 4 decimal places.

    P(cos 45°, sin 45°) = (√2/2, √2/2)

    An isosceles right triangle with legs 1: the hypotenuse is √2.

    sin 45° = 1/√2 = √2/2

    xyOP

    P(cos 45°, sin 45°) ≈ (0.7071, 0.7071)

    Highlighted: the projection on the y-axis — sine, y ≈ 0.7071.

    All four functions of 45°
    FunctionExact valueDecimal
    sin 45°√2/2≈ 0.7071
    cos 45°√2/2≈ 0.7071
    tan 45°11
    cot 45°11

    See Also

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    https://calculat.io/en/number/trigonometry/sin--45Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--45">Sin 45 Degrees: Sine of 45° on the Unit Circle - Calculatio</a>Copy
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    Sin 45 Degrees: Sine of 45° on the Unit Circle. sin 45° = √2/2 ≈ 0.7071. The sine is the y-coordinate of the point at 45° on the unit circle.
    https://calculat.io/en/number/trigonometry/sin--45/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    42°≈ 0.6691
    43°≈ 0.6820
    44°≈ 0.6947
    45°√2/2
    46°≈ 0.7193
    47°≈ 0.7314
    48°≈ 0.7431
    Recalculate with different values ↑

    FAQ

    What is sin 45°?

    sin 45° = √2/2 ≈ 0.7071

    How to remember sin 30°, sin 45° and sin 60°?

    Write them as √1/2, √2/2, √3/2: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2. Cosines are the same numbers in reverse order: cos 30° = √3/2, cos 45° = √2/2, cos 60° = 1/2; tan = sin / cos and cot = cos / sin. Here: sin 45° = √2/2 ≈ 0.7071.

    Why does a calculator show 0.8509 for sin 45?

    The calculator is in radian mode (RAD): it takes sin 45 as the sine of 45 radians, sin 45 rad ≈ 0.8509. Switch it to degrees (DEG): sin 45° = √2/2 ≈ 0.7071. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also