Arccos Calculator
Calculate the inverse cosine (arccos) of any value between -1 and 1.
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Table of Contents
Concept
What is Arccos?
The arccos function (also known as inverse cosine) is the inverse of the cosine function. It takes a value between -1 and 1 and returns the angle whose cosine is that value.
Definition:
If y = cos(θ), then θ = arccos(y)
Formula
Arccos Formula
The arccos function can be calculated using the following formula:
Formula:
arccos(x) = θ where -1 ≤ x ≤ 1 and 0° ≤ θ ≤ 180° (or 0 ≤ θ ≤ π in radians)
Values
Common Arccos Values
Special Values
- arccos(1) = 0°
- arccos(0.8660) = 30°
- arccos(0.7071) = 45°
- arccos(0.5) = 60°
- arccos(0) = 90°
- arccos(-1) = 180°
Properties
- Domain: [-1, 1]
- Range: [0°, 180°] or [0, π]
- arccos(-x) = 180° - arccos(x)
- arccos(cos(θ)) = θ for 0° ≤ θ ≤ 180°
Applications
Applications of Arccos
Physics Wave Analysis
Arccos is used in wave analysis to determine phase angles and wave properties.
Engineering Signal Processing
Arccos functions are used in signal processing to analyze and manipulate signals.
Navigation GPS and Location
Arccos is used in GPS systems to calculate angles and positions.
Tools
Trigonometry Calculators
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