arcsine

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The arcsin function allows the calculation of the arc sine of a number. The arcsin function is the inverse function of the sine function.
arcsin(`0`) returns 0

Arcsine

The arcsin function allows the calculation of the arc sine of a number. The arcsin function is the inverse function of the sine 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].

  1. Calculation of the arcsine
  2. 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.

  3. Derivative of arcsine
  4. The derivative of the arcsine is equal to `1/sqrt(1-(x)^2)`.

  5. Antiderivative of arcsine
  6. The antiderivative of the arcsine is equal to `x*arcsin(x)+sqrt(1-(x)^2)`.

  7. Table of remarkable values
  8. 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`

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.
See also
List of related calculators :
  • 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.
  • Trigonometric Calculator : simplify_trig. Calculator wich uses trigonometric formula to simplify trigonometric expression.
  • Cosine : cos. The cos trigonometric function calculates the cos of an angle in radians, degrees or gradians.
  • Cosecant : cosec. The trigonometric function sec allows to calculate the secant of an angle expressed in radians, degrees, or grades.
  • Cotangent : cotan. The cotan trigonometric function to calculate the cotan of an angle in radians, degrees or gradians.
  • Trigonometric expansion : expand_trigo. The calculator makes it possible to obtain the trigonometric expansion of an expression.
  • Trigonometric linearization : linearization_trigo. Calculator that allows to linearize a trigonometric expression.
  • Simplify Calculator : simplify. Calculator wich can simplify an algebraic expression online.
  • Secant : sec. The trigonometric function sec allows to calculate the secant of an angle expressed in radians, degrees, or grades.
  • Sine : sin. The sin trigonometric function to calculate the sin of an angle in radians, degrees or gradians.
  • Tangent : tan. The tan trigonometric function to calculate the tan of an angle in radians, degrees or gradians.