How To Calculate Arctan

Arctangent Formula:

\[ \theta = \arctan\left(\frac{\text{opposite}}{\text{adjacent}}\right) \]

Angle in Radians:

Angle in Degrees:

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1. What is Arctangent?

The arctangent (arctan) is the inverse of the tangent function. It returns the angle whose tangent is the given ratio of opposite to adjacent sides in a right triangle.

2. How Does the Calculator Work?

The calculator uses the arctangent formula:

\[ \theta = \arctan\left(\frac{\text{opposite}}{\text{adjacent}}\right) \]

Where:

\( \theta \) — Resulting angle (radians)
opposite — Length of the side opposite the angle
adjacent — Length of the side adjacent to the angle

Explanation: The function calculates the angle in radians and converts it to degrees for display.

3. Applications of Arctangent

Details: Arctangent is used in trigonometry, physics (especially in vector calculations), computer graphics, and navigation systems.

4. Using the Calculator

Tips: Enter the lengths of the opposite and adjacent sides. The adjacent side must not be zero. Results are shown in both radians and degrees.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between atan and atan2?
A: atan2 takes two arguments (y,x) and returns angle in the correct quadrant, while atan(y/x) only returns values between -π/2 and π/2.

Q2: What is the range of arctangent?
A: The range is between -π/2 and π/2 radians (-90° to 90°).

Q3: How is arctangent related to slope?
A: The arctangent of a slope gives the angle of inclination of a line.

Q4: What happens when adjacent side is zero?
A: The calculator will show an error as division by zero is undefined.

Q5: Can I calculate arctangent for complex numbers?
A: This calculator only handles real numbers. Complex arctangent requires more advanced mathematics.