Sin-1 Calculator

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.

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:

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 s 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!

Here are tools covering inverse trigonometric functions:

• Arcsin calculator;
• Inverse sine calculator;
• Cos-1 calculator;
• Cos inverse calculator; and
• Inverse tangent calculator.