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# Arccos Calculator

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

Arccos

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Table of Content
 1 Arccosine formula: 2 Using inverse cosine to find an angle: 3 Table for arc cosine: 4 Graph of Arccos: 5 Do Arccos and cos cancel? 6 Is SEC the inverse of cos? 7 What is the inverse of tan? 8 Is Arcsin the inverse of sin?
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An online arccos calculator allows you to calculate the $$arccos(x)$$ or inverse of the cosine of a certain number. Furthermore, this inverse cosine calculator has a built-in function to supports the input of decimal numbers such as $$0.5, -0.5$$, and display results in both degrees and radians. Keep on reading to know about arccos formula and how to find arccos. However, take start with some basics!

## What is Arccos?

In trigonometry, the arccosine of $$x$$ or arccos is defined as the inverse cosine function of $$x$$ when $$-1≤x≤1$$. The condition is:

• If the cosine of $$y$$ will be equal to $$x: cos y = x$$.

Then, the arccosine of x will be equal to the inverse cosine function of x, which is equivalent to $$y: arccos x = cos-1 x = y$$. An inverse cosine calculator can handle complex calculations of trigonometry that involve arccos.

### Arccosine Formula:

Inverse cosine equation is:

$$arccos(x) = cos-1(x)$$

An arccos calculator is functioned to follow this equation automatically to deliver accurate results. You don’t need to enter it manually.

## How to Calculate Arccos?

If the cosine of 60° is 0.5 then what will be the arccos?

• Given $$cos (60°) = 0.5$$.
• Apply formula for inverse of cosine and put the values: arccos$$(x) = cos-1(x)$$.
• arccos of $$0.5 is 60°= cos-1(0.5) = 60°$$

However, the use of an inverse cosine calculator is the most standard to deal with this inverse function of trigonometry.

### Using Inverse Cosine to find an Angle?

An angel can be calculated by applying a simple formula manually. However, if you are looking for a more reliable method then an inverse cos calculator is the best available option. The formula to calculate angel using inverse cosine is:

$$Θ = cos-1(adj/hyp)$$

In such trigonometric functions, $$theta (Θ)$$ will always be the input, and the output will be the ratio of the sides of a triangle.  If this ratio is given and you are required to calculate the angle, you must give a try to above inverse trig function.

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

$$Cos () = a/c = 30/26= 0.866$$

So the inverse function is  = $$arccos (0.866) = 30 degree or 0.52356 radian$$.

However, An online arcsin calculator allows you to determine the arcsin(x) and display the results in radians, degrees, and other relevant units.

## Table for arc cosine:

For easy and fast calculation of arccos, you need to account for a free arccos calculator. Another way is the use of tables that include the common arccos values. Here is the 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/5 1 0° π/6

## Graph of Arccos:

With the help of the graph, we can easily obtain a one-to-one function that has an inverse of cosine. It also helps to display the functions that cannot be obtained algebraically. The graph of arccos is given below:

## How Arccos Calculator Works?

This calculator for arccosine offers a user-friendly and reliable interface that very easy to use for the layman. Follow the simple steps below:

Input

• To find the inverse of cosine, enter “$$x$$” as a real number. It should be within the domain of arccosine calculator function such that $$-1 ≤ x ≤ 1$$.
• Now enter the number of desired decimal places.
• Hit the calculate button

Output

• It will give you two answers. The first one will be an angle in degrees and the second one will be an angel in radians.
• Secondly, it will display results in other units like gradian, turns, minutes and seconds of arc, milliradians, microradian and pi (π) radians.
• In the end, it will give you a detailed calculation.

Furthermore, a unit circle calculator can help you to find the sine, cosine, and tangent values for an angle that helps to figure out different coordinates on the unit circle.

## FAQs:

### Do Arccos and Cos cancel?

While dealing with arccosine and cosine one should keep in mind that they can cancel each other. However, there is a problem with the domain. If dealing with Arccos(x) then it will be defined within the domain of $$[-1,1]$$ . It depicts that you can’t plug in anything that is smaller than -1 or higher than 1. Furthermore, Cos(arccos(x)) is a composite function as well. Additionally, it is recommended to take help from arccos calculator while dealing with arc cosine.

### Is SEC the inverse of Cos?

Secant (SEC) is the reciprocal of the cosine. It can be defined as the ratio of the hypotenuse to the side adjacent.

### What is the inverse of Tan?

The inverse of tan is known as “arctangent”. Arctan is another name to represent it in trigonometry.

### Is Arcsin the inverse of Sin?

In trigonometry, the inverse of sine is known as the arcsin. It is known to returns the angle whose sine is a given number.

## EndNote:

Well, thanks to arccos calculator that provides the full support while calculating inverse cosine. On the other hand, for all of those who are eager to learn and want to have a strong command of trigonometry, it is a great help. Also, if you’re a bit confused, about arccos just get your hands on this cos inverse calculator as it is equally beneficial for students and teachers.

## Reference:

From the Source of Wikipedia: Notation, Principle Values, Relationship among the inverse trigonometric functions.

From the Source of The Math Page: The Inverse Cosine Function, Inverse of trigonometric functions, Inverse Relations.

From the Source of CliffsNotes: Inverse Cosine Function and Equation, Principal values.