### Find the Sine of an Angle with Excel's SIN Function

### Finding the Sine of an Angle in Excel

The trigonometric function *sine*, like the cosine and the tangent, is based on a right-angled triangle (a triangle containing an angle equal to 90 degrees) as shown in the image above.

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 since you no longer have to remember which side of the triangle is adjacent to the angle, which is opposite, and which is the hypotenuse.

### Degrees vs. Radians

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, the angle needs to be in *radians *rather than *degrees *- which is the unit most of us are not familiar with.

Radians are related to the radius of the circle with one radian being approximately equal to 57 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.

Other options for converting from degrees to radians include:

- nesting the RADIANS function inside the SIN function - as shown in row 3 in the example;
- using Excel's
*PI function*in the formula:*angle(degrees) * PI()/180*as shown in row 4 in the example.

### The SIN Function's Syntax and Arguments

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:

*= SIN ( Number )*

Number - 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

### Example: Using Excel's SIN Function

This example cover the steps used to enter the SIN function into cell C2 in the image above 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 function's dialog box - as outlined below.

### Entering the SIN Function

- Click on cell C2 in the worksheet - to make it the active cell;
- Click on the
*Formulas*tab of the ribbon menu; - Choose
*Math & Trig*from the ribbon to open the function drop down list; - Click on
*SIN*in the list to bring up the function's dialog box; - In the dialog box, click on the
*Number*line; - Click on cell B2 in the worksheet to enter that cell reference into the formula;
- Click OK to complete the formula and return to the worksheet;
- The answer 0.5 should appear in cell C2 - which is the sine of a 30 degree angle;
- When you click on cell C2 the complete function
*= SIN ( B2 )*appears in the formula bar above the worksheet.

### #VALUE! Errors and Blank Cell Results

- 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 - row six above. Excel's trig functions interpret blank cells as zero, and the sine of zero radians is equal to zero.

### Trigonometric Uses in Excel

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

Architects, for example use trigonometry for calculations involving sun shading, structural load, and, roof slopes.