Calculation: Arctan Calculator is a tool used to compute the arctangent or inverse tangent of a given value. The arctangent function helps in determining the angle whose tangent is a given number, making it important for various applications in mathematics, physics, and engineering.
What is the purpose of the Arctan Calculator?
The Arctan Calculator is used to find the angle (in radians or degrees) whose tangent is a given number. This is particularly useful in trigonometry, geometry, and physics when solving problems involving angles and right-angled triangles.
Arctan Calculator formula
To calculate the arctangent of a number, you use the formula:
Arctan(x) = y, where tan(y) = xIn other words, the arctangent is the inverse of the tangent function. It returns the angle in radians or degrees whose tangent is equal to the input value (x).
The arctangent of a number is often represented as:
Arctan(x) = θ, where -π/2 ≤ θ ≤ π/2
This formula is used when you need to find the angle in a right-angled triangle when the ratio of the opposite side to the adjacent side is known.
Arctan Calculator examples?
Example 1: Arctan Calculation (Positive Value)
- Suppose a number is given: x = 1
- To calculate Arctan(1), we take the inverse of the arctangent function:
Arctan(1) = 45° or π/4 radians - Result: When the given number is 1, the arctan value is 45° or π/4 radians.
Example 2: Arctan Calculation (Negative Value)
- Now, suppose x = -1 is given.
- To calculate Arctan(-1), we take the inverse of the arctangent function:
Arctan(-1) = -45° or -π/4 radians - Result: When the given number is -1, the arctan value is -45° or -π/4 radians.
These examples clearly demonstrate how the arctan function is calculated and the results for different values. Arctan calculation is commonly used in trigonometry and geometry courses.
Using the Arctan Calculator allows you to accurately calculate angles and helps you with trigonometry problems.