# Documentation/Calc Functions/SIN

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SIN

Mathematical

## Summary:

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

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.

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:

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

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

SIN