Cosine is one of the basic functions in Trigonometry and manual calculations are generally hard to perform. Excel provides an easy way of calculating the cosine through the COS function. This tutorial will assist all levels of Excel users in the usage and syntax of COS function.
Figure 1. Final result: Excel COS function
Formula 1: =COS(RADIANS(B3))
Formula 2: =COS(B3*PI()/180)
Syntax of COS Function
COS function returns the cosine of an angle
=COS(number)
- number – an angle in radians for which we want the cosine
- If an angle is given in degrees, convert it to radians by using the RADIANS function or multiplying the angle by PI()/180
Syntax of RADIANS Function
RADIANS function converts an angle in degrees into radians
=RADIANS(angle)
- angle – an angle in degrees that we want to convert to radians
Setting up our Data
Our table contains two columns: Angle (column B) and Cosine of Angle (column C). We want to determine the cosine of the angles in column B by using the COS function. The results will be recorded in column D.
Figure 2. Sample data for Excel COS function
The COS function calculates the cosine of an angle in radians. Since angles are normally given in degrees form, we have to convert the angle into radians first. There are two ways to do this:
- by using the RADIANS function
- by multiplying the angle in degrees by PI()/180
Calculate cosine of angle converted through RADIANS
We want to calculate the cosine of an angle by using the COS function in combination with the RADIANS function. Let us follow these steps:
Step 1. Select cell C3
Step 2. Enter the formula: =COS(RADIANS(B3))
Step 3. Press ENTER
Step 4: Copy the formula in cell C3 to cells C4:C6 by clicking the “+” icon at the bottom-right corner of cell C3 and dragging it down
Figure 3. Entering the formula using COS and RADIANS
Our formula first converts the angle in degrees into radians through the RADIANS function, then calculates the cosine of the angle that is now in radians. As a result, the value in cell C3 is -0.5.
Below table shows the cosine of the angles using the COS and RADIANS functions.
Figure 4. Cosine of angles calculated using COS and RADIANS
Calculate cosine of angle converted by PI()/180
The alternative to converting angles in degrees into radians is by multiplying the angle with PI()/180. In order to calculate the cosine of an angle by using the COS function in combination with the conversion factor, let us follow these steps:
Step 1. Select cell C3
Step 2. Enter the formula: =COS(B3*PI()/180)
Step 3. Press ENTER
Step 4: Copy the formula in cell C3 to cells C4:C6 by clicking the “+” icon at the bottom-right corner of cell C3 and dragging it down
Figure 5. Entering the formula using COS and conversion factor
Our formula converts the angle in degrees into radians through the conversion factor, then calculates the cosine of the angle through the COS function. As a result, the value in cell C3 is -0.5, which is the same as in the previous example.
The table below shows the cosine of the angles using the COS and the conversion factor “PI()/180”. As we can see, the resulting cosine values are the same as in the first method using COS and RADIANS.
Figure 6. Cosine of angles calculated using COS and conversion factor
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