cosine

radian degree grade

Cosine : How to use it?

The cos trigonometric function calculates the cos of an angle in radians, degrees or gradians.

Syntax :

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

Examples :

cos(`0`), returns 1

Derivative cosine :

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

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

Antiderivative cosine :

Antiderivative calculator allows to calculate an antiderivative of cosine function.

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

Limit cosine :

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

The limit of cos(x) is limit(`cos(x)`)

Inverse function cosine :

The inverse function of cosine is the arccosine function noted arccos.

Graphic cosine :

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

Property of the function cosine :

The cosine function is an even function.

Cosine function

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

The trigonometric function cosine noted cos, allows to calculate the cosine of an angle online , it is possible to use different angular units : degrees, gradians and radians wich is the angular unit by default.

Calculation of the cosine

Cosine calculating an angle in radians

The cosine calculator allows through the cos function to calculate online the cosine 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 cosine online of `pi/6`, enter cos(`pi/6`), after calculation, the result `sqrt(3)/2` is returned.

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

Calculate the cosine of an angle in degrees

To calculate the cosine 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 cosine of 90, enter cos(90), after calculation, the restults 0 is returned.

Calculate the cosine of an angle in gradians

To calculate the cosine 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 cosine of 50, enter cos(50), after computation, the result `sqrt(2)/2` is returned.

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

Special cosine values

The cosine admits some special values which the calculator is able to determine in exact forms. Here is the list of the special cosine values:

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

Main properties

`AA x in RR, k in ZZ`,

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

Derivative of cosine

The derivative of the cosine is equal to -sin(x).

Antiderivative of cosine

The antiderivative of the cosine is equal to sin(x).

Properties of the cosine function

The cosine function is an even function, for every real x, `cos(-x)=cos(x)`. The consequence for the curve representative of the cosine function is that it admits the axis of the ordinates as axis of symmetry.

Equation with cosine

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