Use Excel SIN Function to Find the Sine of an Angle

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The trigonometric function sine, like the cosine and the tangent, is based on a right-angled triangle. In math class, the sine of an angle is found by dividing the length of the side opposite the angle by the length of the hypotenuse.

In Excel, the sine of an angle can be found using the SIN function as long as that angle is measured in radians. Using the SIN function can save you a great deal of time and possibly a great deal of head-scratching.

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Working with Degrees vs. Radians

Screenshot of Excel showing the SIN function in use

Using the SIN function to find the sine of an angle may be easier than doing it manually, but, as mentioned, it is important to realize that when using the SIN function, that the angle needs to be in radians rather than degrees.

To make it easier to work with SIN and Excel's other trig functions, use Excel's RADIANS function to convert the angle being measured from degrees to radians as shown in cell B2 in the image above where the angle of 30-degrees is converted into 0.523598776 radians.

Another option to convert degrees into radians is by using Excel's PI function in the formula as shown in row 4 in the example image.


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SIN Function Syntax and Arguments

Screenshot of Excel showing the Formula Builder

A function's syntax refers to the layout of the function and includes the function's name, brackets, and arguments. The syntax for the SIN function is as follows:

= SIN ( Number )

The number is the angle being calculated, measured in radians. The size of the angle in radians can be entered for this argument or the cell reference to the location of this data in the worksheet can be entered instead.

Using Excel's SIN Function

This example covers the steps used to enter the SIN function into cell C2 to find the sine of a 30-degree angle or 0.523598776 radians.

Options for entering the SIN function include manually typing in the entire function =SIN(B2), or using the Formula Builder, as outlined below.

  1. Click on cell C2 in the worksheet to make it the active cell.
  2. Click on the Formulas tab of the ribbon menu.
  3. Choose Math & Trig from the ribbon to open the function drop-down.
  4. Click on SIN in the list to bring up the Formula Builder.
  5. Click on the Number line.
  6. Click on cell B2 in the worksheet to enter that cell reference.
  7. Click Done to complete the formula.
  8. The answer 0.5 should appear in cell C2, which is the sine of a 30-degree angle.
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#VALUE! Errors and Blank Cell Results

Screenshot of Excel showing an error in the SIN function

The SIN function displays the #VALUE! error if the reference used as the function's argument points to a cell containing text data row five of the example where the cell reference used points to the text label: Angle (Radians).

If the cell points to an empty cell, the function returns a value of zero as shown in row six above. Excel's trig functions interpret blank cells as zero, and the sine of zero radians is equal to zero.