1. What is Arcsin Function?

The arcsin function (also called inverse sine) is the inverse of the sine function. It returns the angle whose sine is the given number. The output is typically in radians between -π/2 and π/2.

2. How Does the Calculator Work?

The calculator uses the PHP asin() function to calculate the inverse sine:

Where:

• \( x \) — Input value between -1 and 1
• \( \theta \) — Result in radians

The calculator also converts the result from radians to degrees using the formula: \[ \text{degrees} = \text{radians} \times \frac{180}{\pi} \]

3. Mathematical Explanation

Special Case: For x = -1/2, arcsin(-1/2) = -π/6 radians or -30°.

This is because sin(-π/6) = -1/2, making -π/6 the principal value of arcsin(-1/2).

4. Using the Calculator

Tips: Enter any value between -1 and 1 inclusive. The calculator will return the corresponding inverse sine value in both radians and degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of arcsin function?
A: The arcsin function returns values in the range [-π/2, π/2] radians or [-90°, 90°].

Q2: Why is arcsin(-1/2) equal to -π/6?
A: Because sin(-π/6) = -1/2, and -π/6 is within the principal range of the arcsin function.

Q3: Can I calculate arcsin for values outside [-1, 1]?
A: No, the arcsin function is only defined for values between -1 and 1 inclusive.

Q4: What are the common arcsin values?
A: Common values include arcsin(0) = 0, arcsin(1/2) = π/6, arcsin(√2/2) = π/4, arcsin(√3/2) = π/3, and arcsin(1) = π/2.

Q5: How is arcsin different from sin⁻¹?
A: They are the same function. arcsin and sin⁻¹ both represent the inverse sine function.