Arcsin Arccos Arctan Calculator

Inverse Trigonometric Functions:

\[ \arcsin(x) = \sin^{-1}(x) \] \[ \arccos(x) = \cos^{-1}(x) \] \[ \arctan(x) = \tan^{-1}(x) \]

Input Value (x):

unitless

Function Type:

Output Unit:

Result:

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1. What are Inverse Trigonometric Functions?

Inverse trigonometric functions (arcsin, arccos, arctan) are the inverse operations of the basic trigonometric functions. They return the angle whose trigonometric function equals the given number. For example, arcsin(0.5) gives the angle whose sine is 0.5.

2. How Does the Calculator Work?

The calculator uses mathematical functions to compute:

\[ \arcsin(x) = \sin^{-1}(x) \] \[ \arccos(x) = \cos^{-1}(x) \] \[ \arctan(x) = \tan^{-1}(x) \]

Where:

\( x \) — Input value (must be between -1 and 1 for arcsin and arccos)
Result can be displayed in radians or degrees

Explanation: The calculator uses PHP's built-in trigonometric functions (asin, acos, atan) and converts the result to the desired unit.

3. Applications of Inverse Trig Functions

Details: Inverse trigonometric functions are essential in mathematics, physics, engineering, and computer graphics for solving triangles, calculating angles, and transforming between coordinate systems.

4. Using the Calculator

Tips: Enter a numeric value, select the desired inverse function (arcsin, arccos, or arctan), and choose output unit (radians or degrees). Note that arcsin and arccos require inputs between -1 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of arcsin and arccos outputs?
A: arcsin outputs values between -π/2 and π/2 radians (-90° to 90°). arccos outputs values between 0 and π radians (0° to 180°).

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

Q3: Why are there restrictions on input values?
A: Sine and cosine functions only produce outputs between -1 and 1, so their inverses can only accept inputs in that range.

Q4: When should I use radians vs degrees?
A: Use radians for mathematical calculations and degrees for practical applications. Most programming languages use radians by default.

Q5: Are there other inverse trigonometric functions?
A: Yes, there are also arccsc, arcsec, and arccot, but arcsin, arccos, and arctan are the most commonly used.