# Sin-1 Calculator

Table of contents

What is sin-1 in math?Inverting the sine functionHow to use this sin-1 calculator?Related Omni calculatorsFAQsWe've built this sin-1 calculator to help you deal with inverting the sine function. Just input a number and get the result! And if you want to learn more about the sin-1 function and its properties, scroll down!

## What is sin-1 in math?

The expression sin-1 may mean two very different things:

**sin-1(x) = 1/sin(x)**, i.e., the multiplicative inverse of value sin(x); or**sin-1(x) = arcsin(x)**, i.e., the**inverse function of the sine**. We're dealing here with the problem of*determining the angle whose sine is equal to*.**x**

We assume that you've come here with the latter meaning in mind. This is because the multiplicative inverse is very easy to determine by performing a simple division, while inverting the sine is quite non trivial.

## Inverting the sine function

The inverse of the sine function, denoted by `arcsin`

, describes the angle that led to a particular sine value:

**arcsin(x) = y if and only if x = sin(y)**.

However, we can only calculate arcsine for numbers from the interval **[-1, 1]**. This is because sine assumes values between -1 and 1.

As for the values assumed by `arcsin(x)`

, they fill in the interval in radians [-π/2, π/2] (equal to [-90°, 90°] in degrees). In other words, this interval constitutes the **range of sin-1**. This is because the sine function must be restricted before inverting to an interval where it is bijective (one-to-one), and the most popular choice is [-π/2, π/2].

And here's the graph of the sin-1 function: you can see both the domain and the range:

## How to use this sin-1 calculator?

Omni's sin-1 calculator is very user-friendly! Just **enter the argument x** and the value of

`sin-1(x)`

will appear immediately. Remember you must enter the value **between -1 and 1**!

Note that our tool can ***convert between radians and degrees**. You don't need to search for any additional tools!

*Tip*: one of the great features of Omni calculators is that they can **work in reverse**. And this sin-1 calculator can do that too! This means that you can use it as a sine calculator as well!

### What is sin-1 of zero?

The answer is **zero**, that is, **sin-1(0) = 0**. To arrive at this result, it's best to re-formulate the question: what is the angle that lies in the interval [-π/2, π/2] and its sine equals zero? A quick look at the graph of the sine function tells us that this angle is indeed zero, as we've claimed.

### How do I determine sin-1 of a negative number?

To determine the sine inverse of a negative number `-x`

:

- Take the
**absolute value**of your number (i.e., remove the minus sign):`x`

. - Compute the
**inverse sine**of the value from Step 1:`sin-1(x)`

. Use an online inverse sine calculator if you need help. **Write the minus sign**in front of the value obtained in Step 2:`-sin-1(x)`

.- This is your answer! We've used here the fact that sin-1 is an
**antisymmetric function**:`sin-1(-x) = -sin-1(x)`

.