arcsine

Quizzes and games : function

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

Quizzes and games : function

Arcsin, online calculus

Summary :

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 online

Description :

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.
Calculate online with arcsin (arcsine)
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.

Course reminders, calculators, exercises and games : Trigonometric functions, Real functions