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Arccos Calculator

Arccos Calculator

Arccos

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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.

 

Arccos Calculator Angle

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 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:

Arccos Calculator graph

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.