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The sin trigonometric function lớn calculate the sin of an angle in radians,degrees or gradians.sin(`0`), returns 0
Quizzes and games : function
Summary :The sin trigonometric function khổng lồ calculate the sin of an angle in radians,degrees or gradians.
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description :Sine functionThe calculator allows to lớn use most of the trigonometric functions, it is possible lớn calculate the sine, the cosine & the tangent of an angle through the functions of the same name..
The trigonometric function sine noted sin, allows to lớn calculate the sine of an angle online , it is possible to lớn use different angular units : degree, grade & 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.
lưu ý that the sine function is able to recognize some special angles & 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.
chú ý that the sine function is able to lớn recognize some special angles và 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 khổng lồ cos(x).
Antiderivative of sine
The antiderivative of the sine is equal lớn -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 lớn solve equation with sine of the size cos(x)=a. The calculations khổng lồ 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 lớn 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 lớn 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.
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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 lớn plot sine function in its definition interval.
Property of the function sine : The sine function is an odd function. Calculate online with sin (sine)