Inverse Sine Calculator

Category: Algebra II
- April 27, 2025
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Calculate the angle whose sine equals a given value. The inverse sine (arcsin) function returns the angle in degrees or radians for sine values from -1 to 1.

Input Value

Display Options

About the Inverse Sine Function

The inverse sine function, also known as arcsin or sin-1, returns the angle whose sine is a given value. It is the inverse of the sine function.

Definition

If sin(θ) = x, then arcsin(x) = θ. In other words, arcsin(x) is the angle whose sine equals x.

arcsin(x) = θ such that sin(θ) = x
Properties of Inverse Sine
  • Domain: [-1, 1]
  • Range: [-π/2, π/2] radians or [-90°, 90°]
  • Odd function: arcsin(-x) = -arcsin(x)
  • Special values: arcsin(0) = 0, arcsin(1) = 90°, arcsin(-1) = -90°
Multiple Solutions

Note that for any given sine value, there are infinite angles with that sine. The arcsin function returns the angle in the principal range [-90°, 90°].

For the second solution in the [0°, 180°] range, use: π - arcsin(x) or 180° - arcsin(x).

Applications

The inverse sine function is used in:

  • Calculating angles in triangles when sides are known
  • Physics - determining angles in projectile motion and optics
  • Engineering - determining component vectors
  • Navigation and GPS systems
  • Computer graphics - calculating viewing angles

Inverse Sine Formula:

Given a sine value x, the inverse sine (arcsin) finds the angle θ such that:

arcsin(x) = θ where sin(θ) = x

What is the Inverse Sine Calculator?

The Inverse Sine Calculator is a simple and effective tool that helps you find the angle corresponding to a given sine value. Whether you need the angle in degrees or radians, this calculator provides accurate results quickly. It uses the arcsine function (also called inverse sine) to solve for the angle where the sine of that angle equals the input value.

It is part of a family of calculators like the Inverse Function Calculator and Trigonometry Calculator, designed to assist you in solving mathematical problems with ease.

How to Use the Inverse Sine Calculator

  • Enter a Sine Value: Input a number between -1 and 1.
  • Select Output Unit: Choose whether you want the result in degrees or radians.
  • Choose Decimal Precision: Select how many decimal places you want for the answer.
  • Display Steps: Optionally, you can see the detailed calculation steps.
  • Click "Calculate Inverse Sine": Get your answer instantly along with a visual graph and second solution if applicable.

If you want to start over, simply hit the "Reset" button to clear all inputs and outputs.

Why Use an Inverse Sine Calculator?

Knowing the angle corresponding to a sine value is very useful in fields like mathematics, Physics, engineering, and even computer graphics. Here are some common uses:

  • Solving triangles when some side lengths are known.
  • Determining projectile motion angles in physics problems.
  • Calculating vector components in engineering.
  • Finding camera or object angles in 3D graphics.
  • Checking work for trigonometric problems.

The calculator can also complement Other tools like the Inverse Hyperbolic Sine Calculator for hyperbolic problems or the Logarithm Calculator for logarithmic equations.

Key Features of This Inverse Sine Calculator

  • Handles both degrees and radians output.
  • Allows customization of decimal places.
  • Offers clear calculation steps for better understanding.
  • Visualizes results with helpful graphs.
  • Calculates the principal value and the second possible angle.

FAQs About the Inverse Sine Calculator

What values can I input?

You can input any value between -1 and 1, as these are the valid domain limits for the sine function.

What is the second solution?

Besides the principal value, the sine function can yield a second angle in the 0°–180° range. This tool shows both.

Can I get the answer in both degrees and radians?

Yes, it automatically provides results in both units so you can use the one that fits your needs.

Is this tool the same as an inverse function calculator?

It focuses specifically on solving the inverse sine, but it works alongside other tools such as the Inverse Function Calculator or Inverse Tangent Calculator when solving broader inverse problems.

How is it different from a regular sine calculator?

A regular Sine Calculator finds the sine of an angle. This Inverse Sine Calculator does the opposite: it finds the angle from a sine value.

Related Tools You Might Find Useful

Using this inverse sine tool helps you solve problems faster and understand trigonometric relationships better, especially when paired with tools like the Polynomial Roots Calculator or Evaluate Calculator for comprehensive Math solutions.