Arcsine : How to use it?
The arcsin function allows the calculation of the arc sine of a number. The arcsin function is the inverse function of the sine function.
Syntax :
arcsin(x) where x is a number.
Other notation sometimes used : asin
Examples :
arcsin(`0`) returns 0
Derivative arcsine :
To differentiate function arcsine online, it is possible to use the derivative calculator which allows the calculation of the derivative of the arcsine function
The derivative of arcsin(x) is derivative(`"arcsin"(x)`)=`1/sqrt(1-(x)^2)`
Antiderivative arcsine :
Antiderivative calculator allows to calculate an antiderivative of arcsine function.
An antiderivative of arcsin(x) is antiderivative(`"arcsin"(x)`)=`x*"arcsin"(x)+sqrt(1-(x)^2)`
Limit arcsine :
The limit calculator allows the calculation of limits of the arcsine function.
The limit of arcsin(x) is limit(`"arcsin"(x)`)
Inverse function arcsine :
The inverse function of arcsine is the sine function noted sin.
Graphic arcsine :The graphing calculator is able to plot arcsine function in its definition interval.
Property of the function arcsine :
The arcsine function is an odd function.Arcsine function
The arcsine function is the inverse function of the sine function, it allows to calculates the arc sine of a number online.
The number on which you wish to apply the arcsine function must belong to the range [-1,1].
Calculation of the arcsine
To calculate the arcsine of a number, just enter the number and apply the arcsin function. Thus, for calculating the arcsine of the number following 0.4, you must enter arcsin(`0.4`) or directly 0.4, if the arcsin button already appears, the result 0.411516846067 is returned.
Derivative of arcsine
The derivative of the arcsine is equal to `1/sqrt(1-(x)^2)`.
Antiderivative of arcsine
The antiderivative of the arcsine is equal to `x*arcsin(x)+sqrt(1-(x)^2)`.
Table of remarkable values
| arcsin(`-1`) | `-pi/2` |
| arcsin(`-sqrt(3)/2`) | `-pi/3` |
| arcsin(`-sqrt(2)/2`) | `-pi/4` |
| arcsin(`-1/2`) | `-pi/6` |
| arcsin(`0`) | `0` |
| arcsin(`1/2`) | `pi/6` |
| arcsin(`sqrt(2)/2`) | `pi/4` |
| arcsin(`sqrt(3)/2`) | `pi/3` |
| arcsin(`1`) | `pi/2` |
- Arccosine : arccos. The arccos function allows the calculation of the arc cosine of a number. The arccos function is the inverse functions of the cosine function.
- Arcsine : arcsin. The arcsin function allows the calculation of the arc sine of a number. The arcsin function is the inverse function of the sine function.
- Arctangent : arctan. The arctan function allows the calculation of the arctan of a number. The arctan function is the inverse functions of the tangent function.
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- Tangent : tan. The tan trigonometric function to calculate the tan of an angle in radians, degrees or gradians.