π Part 1: Introduce
π Definition The TAN function in Microsoft Excel returns the tangent of a given angle.
π― Purpose The function is primarily used to compute the tangent of an angle, which is a fundamental trigonometric function.
π§ Syntax & Arguments
syntax
TAN(number)
- Number: The angle in radians for which you want the tangent.
π Explain the Arguments in the function
- Number: This is a required argument. It represents the angle in radians for which the tangent needs to be calculated.
π Return value The function returns the tangent of the specified angle.
π‘ Remarks If your angle is in degrees, multiply it by PI()/180 or use the RADIANS function to convert it to radians.
π Part 2: Examples
π’ Example 1: Calculating the Tangent of an Angle in Radians
- π― Purpose: To compute the tangent of an angle given in radians.
- π Datasheet and formulas:
| A | B | C | |
|---|---|---|---|
| 1 | Angle (Radians) | TAN Formula | Result |
| 2 | 0.785 | =TAN(A2) | 0.99920 |
- π Explanation: This example demonstrates how to use the TAN function to calculate the tangent of an angle provided in radians. The result for an angle of 0.785 radians is approximately 0.99920.
π’ Example 2: Tangent of an Angle in Degrees
- π― Purpose: To compute the tangent of an angle given in degrees.
- π Datasheet and formulas:
| A | B | C | |
|---|---|---|---|
| 1 | Angle (Degrees) | TAN Formula | Result |
| 2 | 45 | =TAN(RADIANS(A2)) | 1 |
- π Explanation: This example demonstrates how to convert an angle from degrees to radians using the RADIANS function and then compute its tangent. The tangent of 45 degrees is 1.
π’ Example 3: Using TAN with PI
- π― Purpose: To compute the tangent of half of Ο (equivalent to 90 degrees).
- π Datasheet and formulas:
| A | B | C | |
|---|---|---|---|
| 1 | Value | TAN Formula | Result |
| 2 | PI()/2 | =TAN(A2) | β |
- π Explanation: Mathematics’s tangent of Ο/2 or 90 degrees is undefined (or infinity). In Excel, this will return a vast number.
π’ Example 4: Negative Angle
- π― Purpose: To compute the tangent of a negative angle.
- π Datasheet and formulas:
| A | B | C | |
|---|---|---|---|
| 1 | Angle (Radians) | TAN Formula | Result |
| 2 | -0.785 | =TAN(A2) | -0.99920 |
- π Explanation: The tangent function is periodic and odd, meaning TAN(-ΞΈ) = -TAN(ΞΈ). Thus, the tangent of -0.785 radians is approximately -0.99920.
π’ Example 5: Tangent of Zero
- π― Purpose: To compute the tangent of zero.
- π Datasheet and formulas:
| A | B | C | |
|---|---|---|---|
| 1 | Angle (Radians) | TAN Formula | Result |
| 2 | 0 | =TAN(A2) | 0 |
- π Explanation: The tangent of 0 radians (or 0 degrees) is 0. This is a fundamental property of the tangent function.
π Part 3: Tips and tricks
- π« Always ensure that the angle you provide to the TAN function is in radians.
- β Use the RADIANS function to easily convert degrees to radians before using them in the TAN function.
- π Regularly check for updates and additional functionalities Microsoft provides for the TAN function.
- β Consider using TAN in combination with other trigonometric functions to derive more meaningful insights from your data.