Inverse Sine Calculator – Find The Exact Value of Arcsin

Inverse Sine Calculator is a free online tool to calculate the exact value of arcsin in degrees or radians.

Arcsine is an inverse trigonometric function, which refers to the inverse function of sine within -π2 to π2. Denoted as arcsin or sin^-1. It is used to find angles based on the trigonometric ratio of the opposite side to the hypotenuse. Therefore, the formula for arcsine is:

sin(θ) = oppositehypotenuse

 

θ = arcsin(oppositehypotenuse)

If the sine function is represented by x and y (as follows)

y = sin(x), x∈[-π2, π2]

Then, the arcsine function can be expressed as:

x = arcsin(y), y∈[-1, 1]

In order to conform to the habit, define x as a variable and y as a dependent variable, so the arcsine function can be replaced by

y = arcsin(x),  x ∈[-1, 1],  y∈[-π2, π2]

Since sine is a periodic function, there cannot be a single-valued inverse function in the domain of sine. Therefore, the domain of the arcsine function can only be limited to the interval [-1, 1]. In this range, x and y are in one-to-one correspondence.

Like sine, connecting each point of arcsine will form a smooth curve, as follows

arcsin graph

Through this curve, we can summarize several characteristics of arcsine

• Domain – The domain of arcsine is between -1 and 1.
• Range – The range of arcsine is -π2 to π2.
• Monotonicity – In the domain, the arcsine increases monotonically
• Odd function – Since arcsin(x) = – arcsin (-x), arcsin is an odd function.

Computing the arcsine by hand is uncommon, usually only some commonly used arcsines are computed.

For example

sin(30°) = 0.5. So, arcsin(0.5) = 30°

 

sin(90°) = 1. Thus, arcsin(1) = 90°

For some unfamiliar values, calculating the arcsine requires the help of an arcsine table or an arcsine calculator. The arcsine table (given below) lists the corresponding relationship between the sine value and the angle, which is convenient for finding the arcsine value. The disadvantage is that the numbers listed in the arcsine table are limited, and some uncommon values may not be found. So, it is recommended to use the arcsine calculator on this page so that you can easily find all arcsine values.

Arcsine Calculator is so easy to use, even for kids. Enter the sine value, and then click the Calculate button to find the arcsine value, which is the angle. By default, the degrees and radians of the angle will be displayed. Note that the range of input values is between -1 and 1. Decimals and fractions are also supported.

In summary, arcsine is a very important inverse trigonometric function. When the sine value is known, the angle value can be easily calculated by the arcsine function. If you don’t know how to calculate it, just use our arcsine calculator. One second to input, one second to get an answer.