Documentation/Calc Functions/SIN

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    Function name:

    SIN

    Category:

    Mathematical

    Summary:

    Calculates the trigonometric sine (sin) of an angle expressed in radians.

    Syntax:

    SIN(Number)

    Returns:

    Returns a real number in the range [-1, 1] that is the trigonometric sine of the specified angle.

    Arguments:

    Number is a real number, or a reference to a cell containing that number, that is the angle in radians whose trigonometric sine is to be calculated.

    • If Number is non-numeric, then SIN reports a #VALUE! error.

    Additional details:

    If your angle is expressed in degrees, either multiply by PI()/180 or use the RADIANS function to convert to radians.

    The formula for the trigonometric sine of x is:

    [math]\displaystyle{ \sin(x)~=~\sum_{n=0}^{\infty }\frac{(-1)^{n}}{(2n+1)!}~x^{2n+1} }[/math]

    The figure below illustrates the function SIN.

    SIN function

    Examples:

    Formula Description Returns
    =SIN(1) Trigonometric sine of 1 radian. 0.841470984807896
    =SIN(D1) where cell D1 contains the number -0.5. Trigonometric sine of -½ radian. −0.479425538604203
    =SIN(PI()/2) Trigonometric sine of π/2 radians. 1
    =SIN(RADIANS(30)) Trigonometric sine of 30°, after first converting the angle from degrees to radians. 0.5
    =DEGREES(ASIN(SIN(RADIANS(60))) An angle of 60° is converted to radians, its sine is taken, then the inverse sine of that value is calculated, and finally the result is converted back to degrees. 60

    Related LibreOffice functions:

    ASIN

    COS

    COT

    CSC

    SEC

    TAN

    ODF standard:

    Section 6.16.55, part 2

    Related (or similar) Excel functions:

    SIN