arcsin(0) = 0°
The arcsine of 0 is 0 degrees.
The arcsine function (arcsin or sin⁻¹) is the inverse of the sine function. It takes a value between -1 and 1 and returns the angle (in degrees) whose sine is that value. This calculator provides instant and accurate arcsine calculations for mathematical, scientific, and engineering applications.
Mathematical Explanation
Arcsine is the inverse sine function: if sin(θ) = x, then arcsin(x) = θ. The domain is [-1, 1] and the range is [-90°, 90°]. Common values: arcsin(0) = 0°, arcsin(0.5) = 30°, arcsin(1) = 90°. The function is also written as sin⁻¹(x) or asin(x).
Frequently Asked Questions
The arcsine function (arcsin or sin⁻¹) is the inverse of the sine function. It takes a value between -1 and 1 and returns the angle whose sine equals that value. For example, arcsin(0.5) = 30° because sin(30°) = 0.5.
arcsin(0.5) equals 30 degrees exactly. This is one of the fundamental inverse trigonometric values that appears frequently in mathematics and engineering.
arcsin(1) equals 90 degrees, which is the maximum angle in the range of the arcsine function. This represents a right angle.
The arcsine function is only defined for values between -1 and 1 because the sine function only produces values in this range. Since arcsine is the inverse of sine, it can only accept values that sine could have produced.
This calculator returns angles in degrees. If you need the result in radians, multiply the degree value by π/180.
Resources & References
Encyclopedia Resources
- Inverse Trigonometric Functions - Wikipedia - Comprehensive guide to arcsine and other inverse trigonometric functions
- Trigonometry - Wikipedia - Learn about trigonometric functions and their inverses
Educational Resources
- Khan Academy - Inverse Trigonometry - Free inverse trigonometry lessons and practice problems
- Math is Fun - Inverse Sine - Interactive arcsine examples and explanations