1. What are Inverse Trigonometric Functions?

Inverse trigonometric functions (arcsin, arccos, arctan) calculate the angle that produces a given trigonometric ratio. They are the reverse operations of the standard trigonometric functions.

2. How Does the Calculator Work?

The calculator uses the following mathematical functions:

Where:

• \( x \) — Input value (must be between -1 and 1 for arcsin and arccos)
• \( \theta \) — Resulting angle in degrees

Explanation: The calculator converts the radian result from PHP's built-in functions to degrees using the rad2deg() function.

3. Understanding Degrees vs Radians

Details: While trigonometric functions in mathematics often use radians, this calculator provides results in degrees (0° to 360°), which are more intuitive for most practical applications.

4. Using the Calculator

Tips: Enter a value between -1 and 1 for arcsin/arccos (any real number for arctan), select the desired inverse function, and click calculate. The result will be displayed in degrees.

5. Frequently Asked Questions (FAQ)

Q1: Why is my input limited to -1 to 1 for arcsin/arccos?
A: The sine and cosine functions only produce outputs between -1 and 1, so their inverses are only defined for inputs in this range.

Q2: What's the range of results for each function?
A: arcsin: -90° to 90°; arccos: 0° to 180°; arctan: -90° to 90°.

Q3: How accurate are the results?
A: Results are accurate to two decimal places, using PHP's built-in trigonometric functions.

Q4: Can I calculate inverse secant, cosecant, or cotangent?
A: This calculator focuses on the three primary inverse functions. Others can be derived from these.

Q5: What about principal values vs general solutions?
A: This calculator provides the principal value (single solution) for each function.