arctan - arcsin
Use this inverse trigonometric functions calculator to compute arctan and arcsin values accurately in degrees or radians. It also evaluates arccos and arctanx with step-by-step results, covering the derivative of arctan and common inverse trig formulas. Whether you need exact angles for class or quick checks for engineering, this tool gives clear, reliable answers.
Calculation Result - arctan, arcsin, arccos
Enter a value and select a unit, then click calculate to get arctan, arcsin, and arccos.
Computes arctan, arcsin, and arccos simultaneously with high precision
arctan and arcsin – Comprehensive Guide
About arctan and arcsin
arctan and arcsin are two of the most widely used inverse trigonometric functions. Given a trigonometric ratio, arctan returns the angle whose tangent is that ratio, while arcsin returns the angle whose sine is that ratio. The arccos function completes the core set, and arctanx is another common notation for the inverse tangent function. These functions are essential in physics, engineering, robotics, and geometry because they allow you to recover an angle from a known ratio. The calculator on this page simultaneously computes arctan, arcsin, and arccos values in degrees or radians, with step-by-step range explanations. It also covers the derivative of arctan and related inverse trig formulas, making it useful for both quick checks and deeper study.
How to Use arctan and arccos
Step 1: Enter a numeric value. For arctan, any real number works; for arcsin and arccos, use a value between -1 and 1. The derivative of arctan is d/dx[arctan(x)] = 1/(1+x²), a key formula in calculus and one of the most searched derivatives of inverse trig functions.
Step 2: Choose degrees or radians from the Result Unit menu. The derivative of arccos is d/dx[arccos(x)] = -1/√(1-x²), which appears frequently in physics, engineering, and implicit differentiation problems. Selecting the correct unit ensures arctan, arcsin, and arccos results match your homework or project requirements.
Step 3: Click Calculate Inverse Trig Functions. The tool returns arctan, arcsin, and arccos values at once, with the exact angular range for each function. It also supports the derivative of arctan and inverse trigonometric functions as a quick reference while solving calculus or geometry problems.
arctan and arcsin FAQ
- What is arctan? arctan, also called inverse tangent, gives the angle whose tangent is a given number. Its principal value range is (-90°, 90°) in degrees or (-π/2, π/2) in radians. The derivative of arctan is 1/(1+x²), and the arctan graph approaches horizontal asymptotes at y = π/2 and y = -π/2. This makes arctan especially useful for finding angles in right triangles and for converting slopes to angles.
- What is arcsin? arcsin, or inverse sine, returns the angle whose sine equals the input value. Its principal value range is [-90°, 90°] in degrees or [-π/2, π/2] in radians. Use arcsin when you know the opposite side and hypotenuse of a right triangle and need the angle. The calculator also computes arccos and arctanx so you can see all three inverse trigonometric functions at the same time.
- What does the arctan graph look like? The arctan graph is a smooth, increasing curve with two horizontal asymptotes at y = π/2 and y = -π/2. It crosses the origin and is symmetric about the origin. Together with arcsin, arccos, and arctanx graphs, the arctan graph helps students visualize domains, ranges, and inverse trigonometric functions behavior. If you need a quick visual, many textbooks plot arctan graph and arccos graph side by side for comparison.