# Documentation/Calc Functions/COS

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COS

Mathematical

## Summary:

Calculates the trigonometric cosine (cos) of an angle expressed in radians.

COS(Number)

## Returns:

Returns a real number in the range [-1, 1] that is the trigonometric cosine 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 cosine is to be calculated.

• If Number is non-numeric, then COS 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 cosine of x is:

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

The figure below illustrates the function COS.

COS function

## Examples:

Formula Description Returns
=COS(1) Trigonometric cosine of 1 radian. 0.54030230586814
=COS(D1) where cell D1 contains the number -0.5. Trigonometric cosine of -½ radian. 0.877582561890373
=COS(PI()*2) Trigonometric cosine of 2π radians. 1
=COS(RADIANS(60)) Trigonometric cosine of 60°, after first converting the angle from degrees to radians. 0.5
=DEGREES(ACOS(COS(RADIANS(60))) An angle of 60° is converted to radians, its cosine is taken, then the inverse cosine of that value is calculated, and finally the result is converted back to degrees. 60

COS