Solve the arcsine function online and get the angle equivalent to its value. Just enter the number between -1 and 1, press the calculate button and you will automatically get the angle in degrees or radians, you can select the unit you like.
In addition, in the calculations section you will obtain different ways of expressing the same resultThis will be very useful in your trigonometry problems.
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Arcosine function, what is it?
The arcsine is the inverse of the sine function.so that by applying arcsen(y), we can find the value of the angle we are looking for. The arcsine of the arcsine is as follows:
arcsin(y) = sin-1(y) = x + 2kπ
By example,If we apply the arcsine of 1, we obtain that the origin angle is 90º.
arcsen(1) = sin-1(1) = 90°
Derivative of arcsine
The derived from arcsen of a function is equal to the derivative of that function divided by the square root of one minus the function squared.
In the figure above you can see the formula for the derivative of arcsen(x) for a better understanding.
arcosene integral
To calculate the integral to the arcsenIn this case, we need to perform a piecewise integration as illustrated in the figure above:
Finally, after applying the corresponding simplifications, we are left with the following:
Calculate arcsine in Excel
If you want to calculating the arcsine function in ExcelHere we explain how you can obtain the equivalent angle of this trigonometric function in both degrees and radians.
We recommend that you watch the video in which we have made several demonstrative examples of how to calculate arcsine in Excel but if you have any doubts, here is how to do it.
Result in radians
By default, the ASENO Excel function to calculate arcsen(y) returns the result in radians. To check it, just type the following formula in a cell of the spreadsheet:
=ASENO(C3)
Result in degrees
If you want the arcsine function returns you the result in degrees, then you have to write the following formula in a free cell:
=DEGREES(ASENO(C3))
In both cases, C3 are the coordinates of the cell in which we have written the value of y (the result of the function sine:) and that, as mentioned above, its value is between -1 and 1.
Arcoseno Table
Below we have compiled the value in a table the most commonly used values of arcsen(x) in trigonometry problems, something that will be very useful to solve any math problem involving this operation.
| y | x=Arcsen(y) | |
|---|---|---|
| Grades | Radians | |
| -1 | -90° | -π/2 |
| -0.8660254 | -60° | -π/3 |
| -0.7071068 | -45° | -π/4 |
| -0.5 | -30° | -π/6 |
| 0 | 0° | 0 |
| 0.5 | 30° | π/6 |
| 0.7071068 | 45° | π/4 |
| 0.8660254 | 60° | π/3 |
| 1 | 90° | π/2 |
Arcoseno from 0
As you have seen in the table above, the arcsine of 0 corresponds to an angle of 0 radians or 0 degrees. To understand it well, you can apply it in the formula or you can also look at the representation of the arcsine function in the interval from -1 to 1.
As shown in the arcsine graph, for zero we see that the function passes through the origin of coordinates.
On the other hand, the arcsen of 1 corresponds to one of the limits of the function and results in an angle of 90º or π/2 if expressed in radians.
How the arcosene calculator works
Our arcsine calculator is very easy to use. Just enter the value of the function (remember that the valid range is from -1 to 1) and press the Calculate button to obtain the corresponding angle.
As an extra, the result can be represented in degrees or radians, which will facilitate the calculations in trigonometry problems.
Arcoseno in Casio calculators
If you have a Casio calculatorYou can also calculate the arcsen very easily by following these instructions.
Turn on the calculator and press the following key combination:
SHIFT → Sin → x → =
Where x is the value of the arcsen(x) you want to calculate. Ah, remember to check whether the calculator is configured in degrees or radians. as the result that will be displayed when you press the = key will depend on this setting.
Depending on the model of Casio calculator you have, the procedure may change, but in most current models this is the case.
