1. What is the Tan Inverse Function?

The tan inverse function (arctangent) calculates the angle whose tangent is the ratio of the opposite side to the adjacent side in a right-angled triangle. It's the inverse operation of the tangent function.

2. How Does the Calculator Work?

The calculator uses the arctangent formula:

Where:

• \( \theta \) — The angle in degrees
• opposite — Length of the side opposite to the angle
• adjacent — Length of the side adjacent to the angle

Explanation: The calculator first computes the ratio of opposite to adjacent sides, then applies the arctangent function to find the angle in radians, which is then converted to degrees.

3. Importance of Angle Calculation

Details: Calculating angles using trigonometric functions is fundamental in geometry, physics, engineering, and navigation. It's essential for determining directions, slopes, and angles in various applications.

4. Using the Calculator

Tips: Enter lengths of the opposite and adjacent sides in the same units. Both values must be positive numbers. The result is given in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What's the range of arctangent results?
A: The arctangent function returns values between -90° and +90° (-π/2 to +π/2 radians).

Q2: How is this different from regular tangent?
A: Tangent gives the ratio of sides given an angle, while arctangent gives the angle given the ratio of sides.

Q3: What if my triangle isn't right-angled?
A: This formula only works for right-angled triangles. For other triangles, you would need to use the Law of Sines or Cosines.

Q4: Can I use negative values for sides?
A: The calculator only accepts positive lengths, as lengths cannot be negative in Euclidean geometry.

Q5: How precise are the results?
A: Results are accurate to 4 decimal places, which is sufficient for most practical applications.