Arcsin Calculator
Calculate the inverse sine (arcsin) of any value between -1 and 1.
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Table of Contents
Concept
What is Arcsin?
The arcsin function (also known as inverse sine) is the inverse of the sine function. It takes a value between -1 and 1 and returns the angle whose sine is that value.
Definition:
If y = sin(θ), then θ = arcsin(y)
Formula
Arcsin Formula
The arcsin function can be calculated using the following formula:
Formula:
arcsin(x) = θ where -1 ≤ x ≤ 1 and -90° ≤ θ ≤ 90° (or -π/2 ≤ θ ≤ π/2 in radians)
Values
Common Arcsin Values
Special Values
- arcsin(0) = 0°
- arcsin(0.5) = 30°
- arcsin(0.7071) = 45°
- arcsin(0.8660) = 60°
- arcsin(1) = 90°
Properties
- Domain: [-1, 1]
- Range: [-90°, 90°] or [-π/2, π/2]
- Odd function: arcsin(-x) = -arcsin(x)
- arcsin(sin(θ)) = θ for -90° ≤ θ ≤ 90°
Applications
Applications of Arcsin
Physics Wave Analysis
Arcsin is used in wave analysis to determine phase angles and wave properties.
Engineering Signal Processing
Arcsin functions are used in signal processing to analyze and manipulate signals.
Navigation GPS and Location
Arcsin is used in GPS systems to calculate angles and positions.
Tools
Trigonometry Calculators
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