Arccos Calculator

Arccos Calculator

Provide required entities (decimal or fraction), and the arccos calculator will instantly compute inverse cosine values for them in radians or degrees.

An online arccos calculator allows you to calculate the \( arccos(x) \) or inverse of the cosine of a certain number. This inverse cosine calculator supports decimal inputs such as 0.5, -0.5, and displays results in both degrees and radians. Keep reading to learn about the arccos formula and how to find arccos. Let's start with the basics!

What is Arccos?

In trigonometry, the arccosine of \( x \), or arccos, is defined as the inverse cosine function of \( x \) when \( -1 \le x \le 1 \). The condition is:

If the cosine of \( y \) equals \( x \): \( \cos y = x \).

Then, the arccosine of \( x \) is equal to the inverse cosine function of \( x \), i.e., \( y: \arccos x = \cos^{-1} x = y \). An inverse cosine calculator can handle complex trigonometry calculations involving arccos.

Arccosine Formula:

Inverse cosine equation is: \( \arccos(x) = \cos^{-1}(x) \). An arccos calculator automatically follows this equation to deliver accurate results.

How to Calculate Arccos?

If the cosine of 60° is 0.5, what is the arccos?

Given \( \cos 60° = 0.5 \)
Apply the inverse cosine formula: \( \arccos(x) = \cos^{-1}(x) \)
So, \( \arccos(0.5) = 60° \)

Using an inverse cosine calculator is the most standard way to deal with this inverse trigonometric function.

Using Inverse Cosine to Find an Angle

An angle can be calculated manually, but an inverse cos calculator provides a reliable method. The formula to calculate an angle is:

\( \Theta = \cos^{-1}(\text{adj}/\text{hyp}) \)

In such a trigonometric function, \( \Theta \) is the output, and the input is the ratio of the sides of a triangle.

Arccos Calculator Angle

According to the definition of cosine, it equals the adjacent side divided by the hypotenuse:

\( \cos(\theta) = a/c = 30/26 = 0.866 \)

The inverse function gives: \( \arccos(0.866) = 30° \) or 0.52356 radians.

Similarly, an online arcsin calculator determines \( \arcsin(x) \) and displays results in radians, degrees, and other units.

Table for Arc Cosine

For quick calculations of arccos, you can use a table of common values or a free arccos calculator. Here is a reference table:

x	arccos(x) (°)	arccos(x) (rad)
-1	180°	π
-√3 / 2	150°	5π/6
-√2 / 2	135°	3π/4
-1/2	120°	2π/3
0	90°	π/2
1/2	60°	π/3
√2 / 2	45°	π/4
√3 / 2	30°	π/6
1	0°	0

Graph of Arccos

The graph helps visualize the one-to-one inverse of the cosine function. It also displays function behavior that is difficult to obtain algebraically.

Arccos Calculator graph

How Arccos Calculator Works

This arccos calculator is user-friendly and reliable. Follow these steps:

Input

Enter a real number \( x \) in the domain \( -1 \le x \le 1 \).
Enter the desired number of decimal places.
Click the calculate button.

Output

Results include an angle in degrees and radians.
Optional display in other units: gradian, turns, minutes/seconds of arc, milliradians, microradians, and π radians.
A detailed calculation summary is provided.

Additionally, a unit circle calculator can help find sine, cosine, and tangent values for an angle and coordinates on the unit circle.

FAQs

Do Arccos and Cos cancel?

Yes, but only within the domain \( [-1,1] \). Cos(arccos(x)) is a composite function. Use an arccos calculator for accuracy.

Is SEC the inverse of Cos?

No, secant (SEC) is the reciprocal of cosine: hypotenuse / adjacent side.

What is the inverse of Tan?

The inverse of tan is arctangent (arctan).

Is Arcsin the inverse of Sin?

Yes, arcsin returns the angle whose sine equals the given number.

EndNote

The arccos calculator provides full support for calculating inverse cosine. It is useful for students, teachers, and anyone learning trigonometry.

Reference

Wikipedia: Inverse Trigonometric Functions

The Math Page: Inverse Cosine Function

CliffsNotes: Principal values and inverse cosine