# TAN Function in Excel

📌 Part 1: Introduce

📖 Definition The TAN function in Microsoft Excel returns the tangent of a given angle.

🎯 Purpose The function is primarily used to compute the tangent of an angle, which is a fundamental trigonometric function.

🔧 Syntax & Arguments

syntax
`TAN(number)`
• Number: The angle in radians for which you want the tangent.

🔍 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.

🔙 Return value The function returns the tangent of the specified angle.

💡 Remarks If your angle is in degrees, multiply it by PI()/180 or use the RADIANS function to convert it to radians.

📌 Part 2: Examples

🔢 Example 1: Calculating the Tangent of an Angle in Radians

• 🎯 Purpose: To compute the tangent of an angle given in radians.
• 📊 Datasheet and formulas:
ABC
20.785=TAN(A2)0.99920
• 📝 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.

🔢 Example 2: Tangent of an Angle in Degrees

• 🎯 Purpose: To compute the tangent of an angle given in degrees.
• 📊 Datasheet and formulas:
ABC
1Angle (Degrees)TAN FormulaResult
• 📝 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.

🔢 Example 3: Using TAN with PI

• 🎯 Purpose: To compute the tangent of half of π (equivalent to 90 degrees).
• 📊 Datasheet and formulas:
ABC
1ValueTAN FormulaResult
2PI()/2=TAN(A2)
• 📝 Explanation: Mathematics’s tangent of π/2 or 90 degrees is undefined (or infinity). In Excel, this will return a vast number.

🔢 Example 4: Negative Angle

• 🎯 Purpose: To compute the tangent of a negative angle.
• 📊 Datasheet and formulas:
ABC
2-0.785=TAN(A2)-0.99920
• 📝 Explanation: The tangent function is periodic and odd, meaning TAN(-θ) = -TAN(θ). Thus, the tangent of -0.785 radians is approximately -0.99920.

🔢 Example 5: Tangent of Zero

• 🎯 Purpose: To compute the tangent of zero.
• 📊 Datasheet and formulas:
ABC