How to find the cosine of an angle using the COS function in Excel

If you need to find the cosine of an angle, use the COS function in Microsoft Excel. Whether the angle is in degrees or radians, this solution works with a few adjustments. Follow this step-by-step guide to learn how to easily take advantage of Excel’s fast math skills.

The instructions in this article apply to Excel 2019, 2016, 2013, 2010, 2007; Excel for Mac, Excel 365, Excel Online, Excel for Android, Excel for iPad, and Excel for iPhone.

Content
  1. Find cosine of an angle in Excel
  2. Understand degrees vs radians
  3. Trigonometric use in Excel
  4. Syntax and Arguments of the Excel COS Function
  5. Use the Excel COS function
  6. Enter the COS function
  7. Troubleshooting Excel COS function

Find cosine of an angle in Excel

The trigonometric cosine function, like sine and tangent, is based on a right triangle (a triangle with an angle equal to 90 degrees), as shown in the figure below.

In math class, the cosine of an angle is determined by dividing the length of the side next to the angle by the length of the hypotenuse. In Excel, the cosine of an angle can be found using the COS function if that angle is measured in radians.

The COS function saves you a lot of time and potentially a lot of headaches because you no longer have to remember which side of the triangle is adjacent to the opposite angle and which side is adjacent to the hypotenuse.

Understand degrees vs radians

Using the COS function to determine the cosine of an angle may be easier than doing it manually, but as mentioned earlier, it is important to understand that when using the COS function, the angle must be in radians. no degrees.

Radians are related to the radius of a circle. A radian is about 57 degrees.

To make working with COS and other Excel trigger functions easier, use the Excel RADIANS function to convert the measured angle from degrees to radians, as shown in cell B2 in the image above. This example converts an angle of 60 degrees to 1.047197551 radians.

Other options for converting degrees to radians include nesting the RADIANS function in the COS function (as shown in line 3 in the sample image) and using the PI function in the formula (as shown in line 4 in the sample image).

Trigonometric use in Excel

Trigonometry focuses on the relationship between the sides and angles of a triangle, and while many of us don’t need to use it on a daily basis, trigonometry has applications in a number of fields, including architecture, physics, engineering, and surveying.

For example, architects use trigonometry to calculate shading, structural load and roof slopes.

Syntax and Arguments of the Excel COS Function

Function syntax refers to the layout of the function and includes the function name, parentheses, and arguments. Syntax for COS function:

 = COS ( Число ) 

Number † The calculated angle in radians. For this argument, you can enter the size of the angle in radians, or you can specify a cell reference instead to find this data on the worksheet.

Use the Excel COS function

The example in this article covers the steps used to enter the COS function in cell C2 in the image above to find the cosine of a 60-degree angle or 1.047197551 radians.

Options for entering a COS function include entering the entire function manually or using the Function Arguments dialog box, as described below.

Enter the COS function

  1. Select cell C2 on the worksheet to make it active.

  2. Select tab formulas on the ribbon bar.

  3. Select Mathematics & Trig on the ribbon to open the features drop-down list.

  4. Select COS in the list to open the Function Arguments dialog box. Excel for Mac opens the Formula Builder.

  5. Place the cursor on the number line in the dialog box.

  6. Select cell B2 on the worksheet to enter that cell reference into the formula.

  7. Select Okay to complete the formula and return to the sheet. Except for Excel for Mac where you choose Finished

  8. The answer 0.5 appears in cell C2, which is the cosine of a 60 degree angle.

  9. Select cell C2 to see the full function in the formula bar above the worksheet.

 = COS (В2) 

Troubleshooting Excel COS function

#WHERE THE! errors

The COS function returns a #VALUE! error if the reference used as the function argument refers to a cell that contains text data. Switch the cell data type to Numbers to correct the error.

Empty cell results

If the cell points to an empty cell, the function returns the value one. Excel trigger functions interpret empty cells as zero and the cosine of zero radians is one. Correct the error by listing your function in the correct cell.

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