Arcsin Calculator

Do you want to find out the value of the inverse sine function? Congratulations you have selected the right calculator. Because our arcsin calculator can calculate inverse sine function.

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Introduction to Arcsin Calculator:

Arcsin calculator is an amazing online source that helps you find the value of an inverse sine function. Our tool provides you with a simplified method for finding the angle value for the arcsine function.

Arcsin Calculator with Steps

Sin inverse calculator is a learning tool that helps teachers, students, and parents to learn the concept of arcsine function. They can understand how to find its angle value and it enhances the curiosity to find sine as well.

What is the Arcsin (Inverse Sine) Function?

Arcsine is a crucial concept of inverse trigonometric geometry which is used to find the angle value of inverse sine functions. It is known as the inverse sine function, arsine, or sin^-1x function.

It is a continuous periodic function in which domain is between [1,-1]. Although the arcsine function has some similar properties as the arccos function it has a drastically different nature or behavior of function than the inverse sine function for the right angle triangle.

Formula of Arcsin Function:

To determine the angle θ in a right triangle, where the opposite side is a and the hypotenuse is c is given as, the arcsin calculator uses the following formula,

$$ sin (\theta) \;=\; \frac{a}{c} $$

$$ \theta \;=\; arcsin (\frac{a}{c}) $$

How to Calculate the Arcsin (Inverse Sine) Function?

The sin inverse calculator uses a step-by-step process to determine the angle of a right triangle based on a given side length. Follow these steps to calculate the arcsine function easily.

Step 1:

Identify the value of x, through which you want to find the arcsine angle value.

Step 2:

Put the value of x into the arcsine(x) function to get the angle value of arcsin.

Step 3:

You can use the trigonometric table to calculate sine inverse function angle value in the solution.

Solved Example of Arcsin(Inverse Sine) Function:

By using the calculator sin inverse, you can visualize the steps involved in solving the arcsine. A solved example can clearly demonstrate the arcsine calculation process.

Example:

Find the angle of the arcsine function at x = 1/2.

Solution:

$$ x \;=\; sin 𝜃 $$

$$ 𝜃 \;=\; arcsine(x) $$

$$ 𝜃 \;=\; arcsine (\frac{1}{2}) $$

$$ 𝜃 \;=\; 30\; (in\; degree) $$

$$ 𝜃 \;=\; 0.5236\; (in\; radian) $$

How to Use Sin Inverse Calculator?

Calculator sin inverse has a user-friendly layout that allows you to calculate arcsin angle value problems.

You just need to put your problem in this inverse sin calculator and follow some simple steps so you can get results without any inconvenience. These steps are:

Enter the length side value of the right angle triangle function that arcsine angle you want to evaluate in the input box.
Recheck your given input value before clicking on the calculate button to get the solution to the arcsine angle value question.
Click on the “Calculate” button to get the solution to inverse sine function problems.
If you want to check the working process behind our sin-1 calculator then use the load example for the calculation to get an idea about its solution.
The “Recalculate” button allows you to evaluate more examples of arcsine function problems as a solution.

Final Result of Calculator Sin Inverse:

Inverse sin calculator provides you with an arcsine problem’s solution as per your input value when you click on the calculate button. It may include as:

Result Box:

When you click on the result button you get the solution to the arcsine value problem from the Inverse of sine calculator.

Steps Box:
Click on the steps option so that you get the solution of arcsine value questions in a step-by-step method.

Advantages of Inverse Sine Calculator:

Sine inverse calculator has multiple advantages that you can avail whenever you use it to calculate inverse sine problems for solution. It only gets the input value x and gives an inverse sine function problem solution.

It is a trustworthy tool as it always provides you with accurate solutions to arcsine function problems.
Inverse of sine calculator is a speedy tool that evaluates arcsin problems with solutions in a couple of seconds.
It is a handy tool that solves arcsine function value problems without putting any type of external effort into the calculation process.
Arcsin calculator is a free tool that allows you to use it to calculate sine inverse problems without taking any fee.
It is an easy-to-use tool, anyone even a beginner can easily use it for the solution of arcsine function problems.
The sin inverse calculator can open on a desktop, mobile, or laptop through the internet to solve inverse sine function problems.

Related References

How would you describe inverse sine function? Explain.
Give some examples of inverse sine:
How to find the inverse sine function?
Explain inverse sine function with the help of examples.

Frequently Ask Questions

Is arcsin and sin⁻¹ the same?

Yes, arcsin and sin⁻¹ are the same functions as both notations refer to the inverse trigonometric function of sine. Both denote the sine function whose angle value is found when the x value is given.

$$ 𝜃 \;=\; sin^{-1}(x) $$

Or,

$$ 𝜃 \;=\; arcsin(x) $$

What is the derivative of arcsin?

The derivative of the arcsine function can be taken using implicit differentiation. Although the inverse sine function has a direct derivative formula you do not need to do complex calculations just use the direct formula of derivation.

Differentiate with respect to x,

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

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

What is arcsin 1/2 in radians?

To find arcsin⁡(1/2) in radians, you need to determine the angle whose sine value is:

$$ 𝜃 \;=\; arcsin(x) $$

$$ Put\; x \;=\; \frac{1}{2} $$

$$ arcsin\; (\frac{1}{2}) \;=\; \frac{π}{6}\; radians $$

What is arcsin equal to?

The arcsine function is equal to sin⁡−1(x), which is the inverse trigonometric function of the sine function. It gives the angle value whose sine is equal to a given number value x.

$$ x \;=\; Sine\; 𝜃 $$

$$ 𝜃 \;=\; arcsin (x) $$

What is arcsin 90 deg?

The arcsin function is defined to find the angle whose sine is a given value function that must lie within the interval [−1,1]. Thus, the value 90 degrees is not a valid input for the arcsin function because it does not fall in the range of [1,-1].

However, the sine of 90 degrees value is 1 if the function is not inverse which means it is valid for the sine function only.

Amanda Jepson

Last Updated February 21, 2024