Arccos Calculator
Calculate inverse cosine (arccosine) values in degrees and radians with step-by-step calculations. Perfect for trigonometry, mathematics, and engineering applications.
Inverse Cosine Calculator
Common Arccos Values
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Inverse Cosine (Arccos)
The inverse cosine function, denoted as arccos or cos⁻¹, is the inverse of the cosine function. It returns the angle whose cosine is the given value, within the principal value range of 0° to 180°.
Arccos Properties
Range: [0°, 180°] or [0, π] radians
If cos(θ) = x, then arccos(x) = θ
arccos(cos(x)) = x (for x in range)
cos(arccos(x)) = x (for x in domain)
Common Arccos Values
| Input Value | Degrees | Radians | Exact Value |
|---|---|---|---|
| 1 | 0° | 0 | 0 |
| √3/2 ≈ 0.866 | 30° | π/6 | π/6 |
| √2/2 ≈ 0.707 | 45° | π/4 | π/4 |
| 1/2 = 0.5 | 60° | π/3 | π/3 |
| 0 | 90° | π/2 | π/2 |
| -1/2 = -0.5 | 120° | 2π/3 | 2π/3 |
| -√2/2 ≈ -0.707 | 135° | 3π/4 | 3π/4 |
| -√3/2 ≈ -0.866 | 150° | 5π/6 | 5π/6 |
| -1 | 180° | π | π |
- Engineering: Calculate angles in mechanical and electrical engineering applications
- Physics: Determine angles in wave analysis, optics, and mechanics problems
- Navigation: Calculate bearing angles and directional measurements
- Computer Graphics: Compute rotation angles and vector orientations
- Trigonometry: Solve inverse trigonometric problems and find angles from ratios
Frequently Asked Questions
What is arccos?
Arccos (inverse cosine) is the inverse function of cosine. If cos(θ) = x, then arccos(x) = θ. It returns the angle whose cosine is the given value, with a range of 0° to 180° (or 0 to π radians).
What is the domain of arccos?
The domain of arccos is [-1, 1], meaning the input value must be between -1 and 1 inclusive. Values outside this range are undefined because cosine values cannot exceed this range.
What is the range of arccos?
The range of arccos is [0°, 180°] in degrees or [0, π] in radians. This is the principal value range for the inverse cosine function, covering the first and second quadrants.