Use this calculator to find the arccosine (inverse cosine) of a number between -1 and 1.
Formula:
Arccos(x) = cos⁻¹(x)The Arccos Calculator by Easy Converters is a free and powerful online tool designed to help you calculate the inverse cosine (arccos or cos-1) of any valid input value. Whether you’re a student, teacher, engineer, or math enthusiast, this calculator gives you accurate results instantly with just one click.
The **arccos**, or **inverse cosine**, is a trigonometric function that tells you the angle whose cosine is a given value. In mathematical terms:
If cos(θ) = x, then arccos(x) = θ
For example: cos(60°) = 0.5 ⇒ arccos(0.5) = 60°
The arccos function is the inverse of the cosine function. It’s used to determine angles when the cosine value is known. The output range of arccos is between:
The standard formula for inverse cosine is:
θ = arccos(x)
Where:
Example 1: arccos(0.5)
Answer: 60° or π/3 radians
Example 2: arccos(–1)
Answer: 180° or π radians
Example 3: arccos(1)
Answer: 0° or 0 radians
| Cos(x) | arccos(x) in Degrees | arccos(x) in Radians |
|---|---|---|
| 1 | 0° | 0 |
| 0.866 | 30° | π/6 |
| 0.707 | 45° | π/4 |
| 0.5 | 60° | π/3 |
| 0 | 90° | π/2 |
| –0.5 | 120° | 2π/3 |
| –1 | 180° | π |
| Cos(x) | Arccos(x) |
|---|---|
| Gives cosine of an angle | Returns angle for a given cosine |
| Input is an angle | Input is a number between –1 and 1 |
| Output is a ratio | Output is an angle |
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Q: What is the domain of arccos?
A: Arccos is only defined for values between –1 and 1 (inclusive).
Q: What is the range of arccos?
A: The output is from 0 to π radians or 0° to 180°.
Q: How is arccos different from cos-1 on a calculator?
A: They are the same – "arccos" and "cos-1" are two notations for the inverse cosine function.
The Arccos Calculator from Easy Converters makes it simple to work with inverse trigonometric functions. Whether you’re plotting angles, analyzing vector directions, or solving triangles, this tool is accurate, fast, and always available. Try it today and simplify your trigonometric tasks!
The arccosine function is a cornerstone of trigonometry. It helps bridge the gap between ratios and angles. Unlike the basic cosine function that takes an angle and returns a ratio, arccos works in reverse—it takes a ratio and returns the corresponding angle.
It is particularly useful in solving right-angled triangles when the adjacent side and the hypotenuse are known. Using arccos, one can easily determine the angle, thus completing the triangle’s full specification.
In the real world, many problems involve unknown angles that must be calculated from lengths or vector projections. For instance:
When working with arccos functions, outputs are typically given in either degrees or radians. Both are valid units of angle, and it’s important to understand their equivalence:
Many calculators and math software use radians by default. For common users or school-level math, degrees might feel more intuitive. The Easy Converters Arccos Calculator allows you to toggle between both.
The **unit circle** is a powerful way to understand the arccos function. On a unit circle (a circle with radius = 1):
Since cosine is symmetrical around the y-axis, arccos only returns values from 0° to 180° (or 0 to π radians) to ensure it remains a function (one input, one output).
As an inverse function, arccos has its own characteristics:
Unlike the cosine function, which is periodic and many-to-one, arccos is restricted to ensure a one-to-one relationship, making it valid as a function.
Developers and data scientists often work with arccos in their code. Many programming languages provide built-in functions to calculate arccos:
Math.acos(x) in JavaScriptmath.acos(x) in Pythonacos(x) in C/C++ using the math.h library
These typically return the result in radians. To convert to degrees, you can use: degrees = radians × (180 / π).
cos(C) = (a² + b² - c²) / (2ab)
C = arccos[(a² + b² - c²) / (2ab)]
θ = arccos[(A • B) / (|A||B|)]
The Arccos Calculator does not store any personal or usage data. You can use it privately, even offline (if cached), without worrying about login screens or ads interrupting your workflow.
This tool is ideal for:
Preparing for an exam or working on complex trigonometric problems? Bookmark this tool to access it whenever you need to verify inverse cosine values. No ads, no clutter — just math made simple.
Whether you’re solving triangles, analyzing vectors, or building a 3D engine, the Easy Converters Arccos Calculator is your reliable math assistant. Try it now — simplify trigonometry and get back to what matters!