1. What is Tan Inverse?

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

2. How Does the Calculator Work?

The calculator uses the arctangent formula:

Where:

• \( \theta \) — Angle in radians
• opposite — Length of the side opposite to the angle
• adjacent — Length of the side adjacent to the angle

Explanation: The function returns the principal value of the angle, between -π/2 and π/2 radians (-90° and 90°).

3. Applications of Tan Inverse

Details: Tan inverse is used in trigonometry, physics, engineering, and computer graphics for calculating angles from known side lengths.

4. Using the Calculator

Tips: Enter lengths of opposite and adjacent sides. Both values must be valid numbers, and adjacent side cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between tan inverse and cotangent?
A: Tan inverse is the inverse function, while cotangent is the reciprocal (adjacent/opposite). They serve different purposes.

Q2: What range does tan inverse return?
A: The principal value is between -π/2 and π/2 radians (-90° to 90°).

Q3: How is this different from other inverse trig functions?
A: Each inverse function (sin⁻¹, cos⁻¹, tan⁻¹) has different input ranges and output ranges.

Q4: What if my angle is in other quadrants?
A: You may need to adjust the result based on the signs of the inputs to get the correct quadrant.

Q5: Why does my calculator show "atan" or "arctan"?
A: These are alternative notations for tan inverse (tan⁻¹).