Calculation: Arccos Calculator is a tool used to calculate the inverse of the cosine function, also known as the arccosine. This function is used to find the angle whose cosine is a given number.
What is the purpose of the Arccos Calculator?
The Arccos Calculator is used to determine the angle (in radians or degrees) whose cosine is a given value. It is particularly helpful in trigonometry and geometry when solving problems involving angles in right-angled triangles.
Arccos Calculator formula
The formula to calculate the arccosine is as follows:
Arccos(x) = y, where cos(y) = xIn other words, the arccosine is the inverse of the cosine function. It returns the angle (y) in radians or degrees whose cosine equals the input value (x).
This function is defined within a range of 0 to π radians or 0° to 180° degrees. The formula can be expressed as:
Arccos(x) = θ, where 0 ≤ θ ≤ π
This formula is used when you know the cosine value of an angle and you need to find the angle itself.
Arccos Calculator examples?
Example 1: Arccos Calculation (Positive Value)
- Suppose a number is given: x = 0.5
- To calculate Arccos(0.5), we take the inverse of the arccosine function:
Arccos(0.5) = 60° or π/3 radians - Result: When the given number is 0.5, the arccos value is 60° or π/3 radians.
Example 2: Arccos Calculation (Negative Value)
- Now, suppose x = -0.5 is given.
- To calculate Arccos(-0.5), we take the inverse of the arccosine function:
Arccos(-0.5) = 120° or 2π/3 radians - Result: When the given number is -0.5, the arccos value is 120° or 2π/3 radians.
These examples clearly demonstrate how the arccos function is calculated and the results for different values. Arccos calculation is commonly used in trigonometry and geometry courses.
Using the Arccos Calculator allows you to accurately calculate angles and helps you with trigonometry problems.