# sine

The sin trigonometric function to calculate the sin of an angle in radians, degrees or gradians.
sin(0), returns 0

### Sin, online calculus

#### Summary :

The sin trigonometric function to calculate the sin of an angle in radians, degrees or gradians.

# Sine function

The calculator allows to use most of the trigonometric functions, it is possible to calculate the sine, the cosine and the tangent of an angle through the functions of the same name..

The trigonometric function sine noted sin, allows to calculate the sine of an angle online , it is possible to use different angular units : degree, grade and radians wich is the angular unit by default.

## Calculation of the sine

### Sine calculating an angle in radians

The sine calculator allows through the sin function to calculate online the sine sine of an angle in radians, you must first select the desired unit by clicking on the options button calculation module. After that, you can start your calculations.

To calculate sine online of pi/6, enter sin(pi/6), after calculation, the result 1/2 is returned.

Note that the sine function is able to recognize some special angles and make the calculations with special associated values in exact form.

### Calculate the sine of an angle in degrees

To calculate the sine of an angle in degrees, you must first select the desired unit by clicking on the options button calculation module. After that, you can start your calculus.

To calculate sine of 90, enter sin(90), after calculation, the restults 1 is returned.

### Calculate the sine of an angle in gradians

To calculate the sine of an angle in gradians, you must first select the desired unit by clicking on the options button calculation module. After that, you can start your calculus.

To calculate sine of 50, enter sin(50), after computation, the result sqrt(2)/2 is returned.

Note that the sine function is able to recognize some special angles and do the calculus with special associated exact values.

## Special sine values table

The sine admits some special values which the calculator is able to determine in exact forms. Here is a table of the commonsine values:

 sin(2*pi) 0 sin(pi) 0 sin(pi/2) 1 sin(pi/4) sqrt(2)/2 sin(pi/3) sqrt(3)/2 sin(pi/6) 1/2 sin(2*pi/3) sqrt(3)/2 sin(3*pi/4) sqrt(2)/2 sin(5*pi/6) 1/2 sin(0) 0 sin(-2*pi) 0 sin(-pi) 0 sin(pi/2) -1 sin(-pi/4) -sqrt(2)/2 sin(-pi/3) -sqrt(3)/2 sin(-pi/6) -1/2 sin(-2*pi/3) -sqrt(3)/2 sin(-3*pi/4) -sqrt(2)/2 sin(-5*pi/6) -1/2

## Main properties

AA x in RR, k in ZZ,

• sin(-x)= -sin(x)
• sin(x+2*k*pi)=sin(x)
• sin(pi-x)=sin(x)
• sin(pi+x)=-sin(x)
• sin(pi/2-x)=cos(x)
• sin(pi/2+x)=cos(x)

## Derivative of sine

The derivative of the sine is equal to cos(x).

## Antiderivative of sine

The antiderivative of the sine is equal to -cos(x).

## Properties of the sine function

The sine function is an odd function, for every real x, sin(-x)=-sin(x). The consequence for the curve representative of the sine function is that it admits the origin of the reference point as point of symmetry.

## Equation with sine

The calculator has a solver which allows it to solve equation with sine of the form cos(x)=a. The calculations to obtain the result are detailed, so it will be possible to solve equations like sin(x)=1/2 or 2*sin(x)=sqrt(2) with the calculation steps.

#### Syntax :

sin(x), where x is the measure of an angle in degrees, radians, or gradians.

#### Examples :

sin(0), returns 0

#### Derivative sine :

To differentiate function sine online, it is possible to use the derivative calculator which allows the calculation of the derivative of the sine function

The derivative of sin(x) is derivative(sin(x))=cos(x)

#### Antiderivative sine :

Antiderivative calculator allows to calculate an antiderivative of sine function.

An antiderivative of sin(x) is antiderivative(sin(x))=-cos(x)

#### Limit sine :

The limit calculator allows the calculation of limits of the sine function.

The limit of sin(x) is limit(sin(x))

#### Inverse function sine :

The inverse function of sine is the arcsine function noted arcsin.

#### Graphic sine :

The graphing calculator is able to plot sine function in its definition interval.

#### Property of the function sine :

The sine function is an odd function.
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.
Other resources