How TAN works in Excel? Best TAN examples

When working with trigonometric functions in Excel, one of the key formulas you’ll often use is the TAN function. Whether you’re an engineer, mathematician, or simply someone handling complex data, understanding how the tangent function works can make a big difference in your calculations.

Understanding the TAN Function in Excel

The TAN function in Excel returns the tangent of an angle provided in radians. Since Excel’s built-in trigonometric functions work with radians rather than degrees, you must convert degrees to radians if necessary.

Here’s the basic syntax of the function:

=TAN(number)

Where number represents the angle in radians.

Converting Degrees to Radians

Since most real-world scenarios involve angles in degrees, Excel provides two main ways to convert degrees into radians:

1. Using the built-in RADIANS function:

=TAN(RADIANS(45))

1. Multiplying manually by PI()/180:

=TAN(45*PI()/180)

Both methods will return the same result, ensuring accuracy in trigonometric calculations.

Best TAN Examples in Excel

Now that we understand the basics, let’s explore some useful examples where the TAN function can be applied.

Basic TAN Function Example

To calculate the tangent of a 30-degree angle:

=TAN(RADIANS(30))

This will return a value of approximately 0.57735.

Using TAN with Cell References

Suppose you have an angle in cell A1 (in degrees), and you want to calculate its tangent:

=TAN(RADIANS(A1))

Calculating the Height of an Object

One common real-world application of the tangent function is determining the height of an object using trigonometry. Suppose you’re measuring the height of a building. You know the distance to the base (50 meters) and the angle of elevation (35 degrees). The formula to calculate the height would be:

=50 * TAN(RADIANS(35))

This will yield a result of approximately 35.01 meters.

Handling Errors in the TAN Function

The TAN function can return errors in specific cases:

- If the angle is 90 degrees or any multiple of 90 degrees, the function will result in an extremely large number or a #NUM! error because tangent is undefined for such angles.
- To prevent such errors, you can use an IF statement:

=IF(MOD(A1,90)=0, "Undefined", TAN(RADIANS(A1)))

Comparison of TAN with Other Trigonometric Functions

Function	Description	Example
`SIN`	Returns the sine of an angle	`=SIN(RADIANS(30))` → 0.5
`COS`	Returns the cosine of an angle	`=COS(RADIANS(30))` → 0.866
`TAN`	Returns the tangent of an angle	`=TAN(RADIANS(30))` → 0.577

Final Thoughts

The TAN function is an essential tool for working with angles and trigonometric calculations in Excel. Whether you’re translating degrees to radians, handling complex geometric computations, or ensuring accuracy in mathematical models, understanding how TAN works will help you master Excel’s trigonometric capabilities.

Other interesting article:

How COS works in Excel? Best COS examples