# The Excel COS Function

Cosine of an Angle

For the simple right-angled triangle below, the cosine of the angle θ, is the ratio of the adjacent side, a, to the hypotenuse, h.

I.e. for the triangle above,

The trig. ratios are discussed further on the Wikipedia Trigonometric Ratios Page
Related Functions:
SIN Function
TAN Function

## Function Description

The Excel COS function calculates the cosine of a given angle.

The syntax of the function is:

COS( number )

Where the number argument is the angle, in radians, that you want to calculate the cosine of.

If your angle is in degrees, you will need to convert it into radians before supplying it to the Cos function.

This can be done by using the Excel Radians function:

An example of this is given below.

## Cos Function Examples

The following spreadsheet shows the Excel Cos Function, used to calculate the cosine of four different angles.

Formulas:
A B
1 =COS( 0.785398163 )  - cos of 0.785398163 Radians
2 =COS( 0 )  - cos of 0 Radians
3 =COS( -PI()/3 )  - cos of -π/3 Radians
4 =COS( RADIANS( -30 ) )  - cos of -30 Degrees
Results:
A
1 0.707106781
2 1
3 0.5
4 0.866025404

Note that in the above examples:

• In cell A3, the Excel Pi function is used to supply the value -π/3;
• In cell A4, the Excel Radians function is used to convert the angle of -30 degrees into radians before it is supplied to the Cos function.

For further information and examples of the Excel Cos function, see the Microsoft Office website.