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Arctan Function:
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The arctan function, denoted as \(\arctan(x)\) or \(\tan^{-1}(x)\), is the inverse of the tangent function. It returns the angle whose tangent is the given number. This function is essential in trigonometry, geometry, and various engineering applications.
The calculator uses the mathematical arctan function:
Where:
Explanation: The calculator computes the inverse tangent of the input value and converts it to the selected unit (degrees or radians) based on user preference.
Details: Arctan calculations are crucial in trigonometry, physics, engineering, computer graphics, and navigation systems. They help determine angles from tangent ratios, which is fundamental in solving right triangle problems and vector calculations.
Tips: Enter any real number value, select your preferred output unit (degrees or radians), and click calculate. The calculator will return the angle whose tangent equals your input value.
Q1: What is the range of arctan function?
A: The arctan function returns values between -π/2 and π/2 radians (-90° to 90°) for all real number inputs.
Q2: How is arctan different from regular tan?
A: Tan function gives the ratio of opposite/adjacent sides for a given angle, while arctan gives the angle for a given opposite/adjacent ratio.
Q3: Can arctan handle negative values?
A: Yes, arctan can accept any real number (positive, negative, or zero) and will return an angle in the appropriate quadrant.
Q4: When should I use degrees vs radians?
A: Use degrees for everyday applications and geometry problems. Use radians for advanced mathematics, physics, and engineering calculations.
Q5: What are common applications of arctan?
A: Arctan is used in computer graphics for rotations, in physics for vector calculations, in engineering for slope calculations, and in navigation for bearing calculations.