### Finding the Sine, Cosine, and Tangent of an Angle in Google Spreadsheets

### Google Spreadsheets Trigonometric Functions

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

In math class, these trig functions are found using various trigonometric ratios comparing the length of the triangle's adjacent and opposite sides with that of the hypotenuse or with each other.

In Google Spreadsheets, these trig functions can be found using the SIN, COS, and TAN functions for angles measured in *radians*.

### Degrees vs. Radians

Using the above trigonometric functions in Google Spreadsheets may be easier than doing it manually, but, as mentioned, it is important to realize that when using the these functions, the angle needs to be measured 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 the trig functions, use Google Spreadsheets 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 0.5235987756 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 Google Spreadsheets
*PI function*in the formula:*angle(degrees) * PI()/180*as shown in row 4 in the example.

### The Trig Functions' 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 ( angle )*

The syntax for the COS function is:

*= COS ( angle )*

The syntax for the TAN function is:

*= TAN ( angle )*

angle - the angle being calculated - measured in radians

- the size of the angle in radians can be entered for this argument or, alternatively, the cell reference to the location of this data in the worksheet.

### Example: Using Google Spreadsheets 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 0.5235987756 radians.

The same steps can be used for calculating the cosine and tangent for an angle as shown in rows 11 and 12 in the image above.

Google Spreadsheets does not use dialog boxes to enter a function's arguments as can be found in Excel. Instead, it has an *auto-suggest* box that pops up as the name of the function is typed into a cell.

- Click on cell C2 to make it the active cell - this is where the results of the SIN function will be displayed;
- Type the equal sign ( = ) followed by the name of the function
*sin;* - As you type, the
*auto-suggest*box appears with the names of functions that begin with the letter S; - When the name
*SIN*appears in the box, click on the name with the mouse pointer to enter the function name and open parenthesis or round bracket into cell C2.

### Entering the Function's Argument

As seen in the image above, the argument for the SIN function is entered after the open round bracket.

- Click on cell B2 in the worksheet to enter this cell reference as the
*angle*argument; - Press the
*Enter*key on the keyboard to enter a closing parenthesis "**)**" after the function's argument and to complete the function; - The value 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. Google Spreadsheets trig functions interpret blank cells as zero, and the sine of zero radians is equal to zero.