Arccos Degrees Calculator

The arccos degrees calculator computes the inverse cosine function, returning the angle in degrees whose cosine is the input value. This is useful in trigonometry, physics, and engineering applications where you need to find angles from known cosine values.

What is Arccos?

The arccosine function, also known as the inverse cosine function, is the inverse of the cosine function. While cosine takes an angle and returns a ratio, arccosine takes a ratio and returns an angle. The range of arccosine is typically 0° to 180° because cosine is periodic and symmetric.

Mathematically, if cos(θ) = x, then θ = arccos(x). The function is defined for x values between -1 and 1, inclusive.

Key Properties

Domain: -1 ≤ x ≤ 1
Range: 0° ≤ θ ≤ 180°
Special cases: arccos(1) = 0°, arccos(0) = 90°, arccos(-1) = 180°

How to Use the Arccos Degrees Calculator

Enter a cosine value between -1 and 1 in the input field.
Click the "Calculate" button to compute the angle in degrees.
View the result displayed in the result panel.
Use the "Reset" button to clear the input and result.

The calculator will display the angle in degrees corresponding to the input cosine value. For values outside the valid range, an error message will appear.

Arccos Formula

Mathematical Formula

θ = arccos(x) × (180° / π)

Where:

θ = angle in degrees
x = cosine value (-1 ≤ x ≤ 1)
π ≈ 3.141592653589793

The formula converts the result from radians (which is the standard output of most programming languages' arccos functions) to degrees by multiplying by 180°/π.

Worked Examples

Example 1: Basic Calculation

Find the angle whose cosine is 0.5.

Using the formula: θ = arccos(0.5) × (180° / π) ≈ 60°

This means cos(60°) = 0.5.

Example 2: Edge Case

Find the angle whose cosine is -1.

Using the formula: θ = arccos(-1) × (180° / π) = 180°

This is the maximum angle in the range of arccos.

Frequently Asked Questions

What is the difference between arccos and cos?

The cosine function (cos) takes an angle and returns a ratio, while the arccosine function (arccos) takes a ratio and returns an angle. They are inverse functions of each other.

What happens if I enter a value outside the valid range?

The calculator will display an error message because the arccosine function is only defined for values between -1 and 1.

Can I use this calculator for radians?

No, this calculator specifically provides results in degrees. For radians, you would need to use a different calculator or convert the result manually.

Is the arccos function the same as the secant function?

No, the arccos function is the inverse cosine function, while the secant function is the reciprocal of the cosine function (sec(x) = 1/cos(x)).