Sin Cos Tan Inverse Calculator

Inverse Trigonometric Functions:

\[ \arcsin(x),\ \arccos(x),\ \arctan(x) \]

Input Value:

Function:

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 trigonometric functions. They take a ratio as input and return an angle as output. These functions are essential in geometry, physics, and engineering.

2. How the Calculator Works

The calculator uses PHP's built-in trigonometric functions:

arcsin(x) = asin(x)
arccos(x) = acos(x)
arctan(x) = atan(x)

The results can be displayed in either radians or degrees. For degrees, the radian result is converted using:

\[ \text{degrees} = \text{radians} \times \frac{180}{\pi} \]

3. Understanding the Results

Range of Results:

arcsin: -π/2 to π/2 radians (-90° to 90°)
arccos: 0 to π radians (0° to 180°)
arctan: -π/2 to π/2 radians (-90° to 90°)

4. Using the Calculator

Tips:

For arcsin and arccos, input must be between -1 and 1
For arctan, any real number is valid
Choose whether you want results in radians or degrees

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between arcsin and sin⁻¹?
A: They are the same function, just different notations. Both represent the inverse sine function.

Q2: Why does arccos give results between 0 and π?
A: This is by definition to make it a proper function (single output for each input).

Q3: Can I calculate inverse cosecant, secant, or cotangent?
A: These can be derived from the basic three: arccsc(x) = arcsin(1/x), etc.

Q4: What's the principal value?
A: The calculator returns the principal (main) value of the inverse function.

Q5: How precise are the results?
A: Results are precise to at least 4 decimal places.