1. What is Arc Tangent?

The arc tangent (arctan) is the inverse function of the tangent. It returns the angle whose tangent is the given number. The output can be in radians or degrees.

2. How Does the Calculator Work?

The calculator uses the arc tangent formula:

Where:

• \( \theta \) — The angle in radians
• \( \text{opposite} \) — Length of the opposite side
• \( \text{adjacent} \) — Length of the adjacent side

Explanation: The calculator computes the angle in a right triangle given the ratio of the opposite to adjacent sides.

3. Applications of Arc Tangent

Details: Arc tangent is widely used in trigonometry, physics, engineering, and computer graphics for calculating angles from coordinate data.

4. Using the Calculator

Tips: Enter the lengths of the opposite and adjacent sides (unitless values). The calculator will return the angle in both radians and degrees.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between radians and degrees?
A: Radians measure angles based on the radius of a circle (2π = 360°), while degrees divide a circle into 360 parts.

Q2: What happens if adjacent side is zero?
A: The calculator will show an error as division by zero is undefined (vertical line, angle = 90°).

Q3: What's the range of arctan output?
A: The output range is between -π/2 and π/2 radians (-90° to 90°).

Q4: How is this different from arcsin or arccos?
A: Each inverse trig function uses different side ratios - arctan uses opposite/adjacent, arcsin uses opposite/hypotenuse, arccos uses adjacent/hypotenuse.

Q5: When would I need to use atan2 instead?
A: Use atan2(y,x) when you need to determine the correct quadrant of the angle based on both x and y coordinates.