Arccos Calculator

Calculate the value of y in an arccos function based on the value of the x variable, quickly and easily using this tool.

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What it is

What is Arccos?

Create Date: August 26, 2024

Last Modified Date: November 19, 2024

Arccos, also known as the inverse cosine function, is used to determine the angle whose cosine value is a given number. It provides the angle in the range of 0° to 180° (or 0 to π radians), which represents the possible angles that have the specified cosine value. This function is fundamental in trigonometry and has practical applications in geometry, physics, engineering, and computer graphics.

How to Calculate Arccos

The arccosine function, written as arccos(x) or cos-1(x), allows us to determine the angle when we know its cosine value. The value of x must be between -1 and 1 since cosine values do not exceed these limits.

  • Arccos(x): Calculates the angle whose cosine is x.

  • For example, if cos(θ) = 0.5, then arccos(0.5) = 60° (or π/3 radians).

Understanding Your Results

The result of an arccos calculation is an angle, typically given in degrees or radians. This angle represents the position where the cosine of the angle equals the value of x you entered. You can use the dropdown menu to easily convert your result into different units of angle measurement, such as degrees, radians, gradians, or turns, depending on your needs.

How to Use the Arccos Tool

This arccos calculator is very simple to use. Just follow these steps:

  1. Enter the value of x, which must be between -1 and 1.

  2. Hit the calculate button to get the corresponding angle value.

  3. Use the dropdown menu to convert the result to your preferred unit (e.g., degrees, radians, etc.).

Example Calculation

Let’s say you want to find the angle whose cosine value is 0.5. You enter 0.5 into the input field, hit calculate, and the tool will return 60° as the answer (or π/3 radians). You can then change the units using the dropdown menu if desired.

Arccos - Frequently Asked Questions

The arccos formula is written as arccos(x) or cos-1(x), and it is used to find the angle whose cosine is equal to the given value x, where -1 ≤ x ≤ 1.

Arccos is used to determine the angle of a right triangle when the adjacent side and hypotenuse are known. It’s also useful in fields like physics, engineering, and computer graphics for resolving direction and angles.

Cosine (cos) takes an angle and returns a ratio between the adjacent side and the hypotenuse of a right triangle. Arccos (inverse cosine) takes a ratio and returns the corresponding angle. Essentially, they are inverse operations.

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