MathematicsTrigonometry
Arccos Calculator
Calculate inverse cosine (arccos) values instantly. Enter any value between -1 and 1 to find the corresponding angle in degrees or radians. Free arccos calculator.
The arcsin calculator helps you find the inverse sine of any number between -1 and 1. Also known as arcsine or sin⁻¹, this trigonometric function returns the angle whose sine equals your input value. Whether you're working in degrees, radians, or other angular units, this calculator provides instant, accurate results for mathematics, physics, and engineering applications.
Arcsin (inverse sine) is a trigonometric function that reverses the sine operation. If sin(θ) = x, then arcsin(x) = θ. The function accepts input values from -1 to 1 and returns angles between -π/2 and π/2 radians (-90° to 90°). This range represents the principal values of the inverse sine function.
In mathematical notation, arcsin is written as sin⁻¹(x) or asin(x). The function is widely used in geometry to find angles in right triangles when side lengths are known, in physics for projectile motion analysis, and in engineering for wave calculations and signal processing.
Using the calculator is straightforward. Enter your known value in either field. If you know the x value (between -1 and 1), enter it to calculate the corresponding angle. If you know the angle, enter it to find the sine value. Select your preferred angle unit from the dropdown menu—degrees, radians, gradians, or turns. The calculator automatically updates results as you type.
Arcsin is essential in right triangle trigonometry, where it calculates angles from opposite-to-hypotenuse ratios. In physics, it helps analyze projectile trajectories, pendulum motion, and wave behavior. Navigation systems use it for altitude calculations and GPS positioning. Computer graphics applications rely on arcsin for lighting effects, animations, and transformations. In engineering, it appears in vibration analysis and AC circuit calculations.
Remember that arcsin only accepts values between -1 and 1 inclusive
The output angle will always be between -90° and 90° (-π/2 and π/2 radians)
Use radians for calculus and advanced mathematics, degrees for everyday applications
Common values: arcsin(0) = 0°, arcsin(1) = 90°, arcsin(-1) = -90°
What is the domain of arcsin?
The domain of arcsin is [-1, 1]. Any input outside this range is undefined because sine values cannot exceed these bounds.
Is arcsin the same as 1/sin(x)?
No. The notation sin⁻¹(x) means inverse sine (arcsin), not 1/sin(x). The reciprocal of sine is called cosecant, written as csc(x).
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