Arccos Calculator

Want to compute the solution of the inverse cosine function then try our Arccos calculator. It can solve your problem according to your given instructions.

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Introduction to Arccos Calculator:

Arccos Calculator is a digital source that is present online that is used to find the given Arccos function value. It gives a systematic way to compute the angle of the inverse cosine function from the given value of x.

Arccos Calculator with Steps

Inverse cosine calculator is a handy tool that can solve various types of inverse cosine function problems and provides you with accurate solutions every time whenever you use it for the evaluation process.

What is the Arccos (Inverse Cosine) Function?

Arccos function is the inverse trigonometric function of cosine which helps you to find the angle value 𝜃 from the given value in the right-hand triangle. It is mathematically denoted as cos^-1, inverse cosine function, or arccos function.

Arccos is an important method in geometry that is used to find the angle of horizontal lines in the right-angle triangle. It is the periodic function whose domain and range are between [1,-1].

Formula of Arccos Function:

The formula of the Arccos function depends on the ratio of adjacent sides b over the hypotenuse side c in the right-angle triangle. Here 𝜃 is the angle of the arccos function. The formula behind the inverse cosine calculator is:

$$ cos (\theta) \;=\; \frac{b}{c} $$

$$ \theta \;=\; arccos (\frac{b}{c}) $$

How to Calculate Arccos (Inverse Cosine) Function?

To calculate the inverse cosine function, the cos inverse calculator uses the rules that you should know for finding the inverse trigonometric function like the arccos function. Let's see a stepwise method about how to find the arccos function value solution.

Step 1:

Identify the value of x for which you need to find the arccos function angle value.

Step 2:

Put the value of x into the cos^-1(x) to get the angle value of the inverse cosine function.

Step 3:

You can use the trigonometric table to find the arccos function value to find an angle in the solution.

Solved Example of Arccos (Inverse Cosine) Function:

A solved example of the arccos function gives you a better understanding of the working procedure of the inverse cosine calculator.

Example:

Find the unknown angle value of the Arcos function as x = 1/2.

Solution:

Given that x = ½

The arccos function is,

$$ y \;=\; cos^{-1}(x) $$

Put x value in it

$$ y \;=\; arccos(\frac{1}{2}) $$

$$ y \;=\; 60 (in\; degree) $$

$$ y \;=\; 1.047198\; (in\; radian) $$

How to Use Inverse Cosine Calculator?

Arc cosine calculator has a user-friendly design that enables you to solve inverse cosine value problems. You just need to follow some simple steps to get a comfortable experience during the evaluation process. These steps are:

Enter the value of x to find the angle of the arccos function in the inverse cos calculator’s input field.
Check the given number value before clicking the calculate button to get the correct solution of the arccos function.
Click the “Calculate” button for the solution of the arccos function value using the trigonometric function.
Click the “Recalculate” button for the calculation of more questions to find out the inverse cosine function angle value.
If you want to check the working behind the cos inverse calculator then use the load example to get an idea about the accuracy of solution.

Output of Arc Cosine Calculator:

Arc cosine calculator provides you with a solution to your input number problem when you click on the calculate button. It may contain as:

In the Result Box:

When you click on the result button of the arccos calculator, you get the solution of the arccos function angle value.

Steps Box:
Click on the steps option so that you get the solution of the arccos function angle value in steps.

Benefits of Cos Inverse Calculator:

Cosine inverse calculator can give you multiple benefits beyond solving the angle value problem of the Arccos function. These benefits are:

Cos-1 calculator is a trustworthy tool as it always provides you with accurate solutions for arccos angle value problem.
It is a fast tool that evaluates the inverse cosine function’s angle value and gives solutions in a couple of seconds.
Arccos Calculator is a free tool that allows you to calculate the given Arccos inverse function angle value problem without any fee. This quality will compel you to choose our tool for getting the solution of the angle value problem.
It has a simple design, so anyone can easily use it to get the solution of arccos value problems.
This Calculator can operate on a desktop, mobile, or laptop through the internet to solve inverse cosine problems.
Cos inv calculator is an educational tool that can be used to teach children about the concept of arccos function with an easy calculation process.

Related References

How would you define arccos function?
Explain the evaluation process of arccos function:
Give some examples of arccos function:
Give an overview of arccos function?

Frequently Ask Questions

What is the derivative of arccos?

The derivative of the arccos function can easily be found because it has a direct formula of derivation. Differentiate the y = arccos(x) with respect to x,

$$ \frac{d}{dx} (arccos (x)) \;=\; - \frac{1}{\sqrt{1-x^2}} $$

$$ \frac{dy}{dx} \;=\; - \frac{1}{\sqrt{1-x^2}} $$

What is arccos 0?

To find arccos⁡(0), you need to determine the angle θ for which the cosine is equal to 0.

$$ x \;=\; cos⁡(θ) $$

$$ θ \;=\; cos(x) $$

$$ For\; x \;=\; 0 $$

$$ θ \;=\; cos(0) $$

$$ θ \;=\; 90° $$

What is the integral of arccos?

To find the integral of the arccosine function, arccos⁡(x), you need to integrate it with respect to x. Here’s how to integrate the inverse function arccos.

$$ y \;=\; arccos\; x $$

Integrate with respect to x and use the integrate-by-parts rule because the inverse function cannot be integrated directly,

$$ \int arccos\; (x)\; dx \;=\; x\; arccos\; (x) - \int x\; (- \frac{1}{\sqrt{1-x^2}} ) dx $$

$$ =\; x\; arccos\; (x) + \int \frac{x}{\sqrt{1-x^2}} dx $$

Apply the u-substitution method to find the second part of an integral. Put it in the above part for integration,

Let u = 1 - x^2, so du = -2x dx, hence x dx = - 1/2 du

$$ \int \frac{x}{\sqrt{1-x^2}} dx \;=\; \int -\frac{1}{2} \frac{du}{\sqrt{u}} $$

$$ =\; - \frac{1}{2} \int u^{-\frac{1}{2}} du $$

$$ =\; - \frac{1}{2} . 2\sqrt{u} + C $$

$$ =\; - \sqrt{1-x^2} + C $$

Put this value in the above expression to get the solution to the Arccos function problem,

$$ \int arccos (x)\; dx \;=\; x\; arccos (x) - \sqrt{1 - x^2} + C $$

What is arccos of 45 degree?

The arccosine function has the range [−1,1]. This is because the cosine of any angle cannot be less than -1 or greater than 1. Since 45 is outside the domain of [−1,1] so arccos ⁡(45) is not defined in the real number system. For real-valued functions, if the input is outside [−1,1], the result is undefined or not a real number.

What is the range of arccos?

The range of arccos is within the interval to ensure that arccos⁡(x) returns a unique angle for each value of x in its domain [−1,1]. This interval is chosen because cosine is a decreasing function on [0,π], within this interval.

Amanda Jepson

Last Updated February 21, 2024