1. What is Inverse Sine?

The inverse sine function (arcsin) is the inverse operation of the sine function. It returns the angle whose sine is a given number. The result is typically expressed in degrees or radians.

2. How Does the Calculator Work?

The calculator uses the inverse sine formula:

Where:

• \( \theta \) — The angle to be calculated
• \( \text{opposite} \) — Length of the side opposite to the angle
• \( \text{hypotenuse} \) — Length of the hypotenuse

Explanation: The calculator computes the ratio of opposite side to hypotenuse, then calculates the inverse sine of that ratio to find the angle.

3. Importance of Inverse Sine Calculation

Details: Inverse sine calculations are essential in trigonometry, geometry, physics, engineering, and computer graphics for determining angles from known side ratios in right triangles.

4. Using the Calculator

Tips: Enter the length of the opposite side and hypotenuse (both must be positive numbers). The hypotenuse must be greater than or equal to the opposite side. Select whether you want the result in degrees or radians.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of valid inputs?
A: The ratio of opposite/hypotenuse must be between -1 and 1. Both values must be positive numbers.

Q2: What is the range of output values?
A: The inverse sine function returns values between -π/2 and π/2 radians (-90° and 90°).

Q3: When should I use degrees vs radians?
A: Use degrees for everyday applications and geometry problems. Use radians for calculus, physics, and advanced mathematics.

Q4: Can I use this for non-right triangles?
A: No, the inverse sine function as shown here applies only to right triangles. For other triangles, use the Law of Sines.

Q5: What if my ratio is greater than 1 or less than -1?
A: This indicates an error in measurement, as the sine of an angle cannot exceed 1 or be less than -1 in a right triangle.