Druyd:Knowledge

Trigonometric Functions

Description

Otherwise, trigonometric functions can be used to describe physical processes that include oscillations.

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Trigonometric functions

Description

Trigonometric functions allow the calculation of the angles of right triangles, or having the angles, calculate the legs of the triangles.

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Value of PI

Image

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Calculation in radians and degrees

Image

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Trigonometric Functions

Description

Trigonometric functions allow you to determine the angles of rectangular triangles based on their sides. In turn they allow the calculation of the sides based on other sides and angles of the triangle.\\nOtherwise, trigonometric functions can be used to describe physical processes that include oscillations.

Variables

Symbol

Text

Variable

Value

Units

Calculate

MKS Value

MKS Units

$a$

Adjacent leg

$\theta$

theta

Angle

rad

$\phi$

phi

Complementary angle

rad

$c$

Hypotenuse

$b$

Sum (2)

Calculations

Equation

Number

First, select the equation:

, then, select the variable:

Symbol

Equation

Solved

Translated

Calculations

Symbol

Equation

Solved

Translated

Variable

Given

Calculate

Target :

Equation

To be used

Equations

$ c ^2= a ^2+ b ^2$

c ^2= a ^2+ b ^2

$\cos \theta =\displaystyle\frac{ a }{ c }$

cos( theta )= a / c

$\sin \theta =\displaystyle\frac{ b }{ c }$

sin( theta )= b / c

$\tan \theta =\displaystyle\frac{ b }{ a }$

tan( theta )= b / a

$\mbox{cot}\theta=\displaystyle\frac{a}{b}$

cot( theta )= a / b

$\theta=\arccos\displaystyle\frac{a}{c}$

\theta=\arccos\displaystyle\frac{a}{c}

$\theta=\arcsin\displaystyle\frac{b}{c}$

\theta=\arcsin\displaystyle\frac{b}{c}

$\theta=\arctan\displaystyle\frac{b}{a}$

\theta=\arctan\displaystyle\frac{b}{a}

$\theta=\arctan\displaystyle\frac{b}{a}$

\theta=arccot\displaystyle\frac{a}{b}

$\tan\theta=\displaystyle\frac{\sin\theta}{\cos\theta}$

\tan\theta=\displaystyle\frac{\sin\theta}{\cos\theta}

$\sin^2 \theta +\cos^2 \theta =1$

sin( theta )^2+cos( theta )^2=1

$\sin( \alpha + \beta ) =\sin \alpha \cos \beta +\cos \alpha \sin \beta $

sin( alpha + beta )=sin( alpha )*cos( beta )+cos( alpha )*sin( beta )

$\cos( \alpha + \beta )=\cos \alpha \cos \beta +\sin \alpha \sin \beta $

cos( alpha + beta )=cos( alpha )*cos( beta )-sin( alpha )*sin( beta )

$\tan( \alpha + \beta ) =\displaystyle\frac{\tan \alpha -\tan \beta }{1-\tan \alpha \tan \beta }$

tan( alpha + beta )=(tan( alpha )+tan( beta ))/(1 -tan( alpha )*tan( beta ))

$ \theta + \phi =\displaystyle\frac{1}{2} \pi$

theta + phi = pi /2

Examples

Trigonometric functions

Trigonometric functions allow the calculation of the angles of right triangles, or having the angles, calculate the legs of the triangles.

Value of PI

Si se requiere el valor de Pi se puede generar el valor con la calculadora:

image

Hay que tener cuidado que al usar un numero de pocos digitos se puede afectar el resultado del calculo.

Calculation in radians and degrees

In many cases it is necessary to work with radians instead of degrees. In these cases it is necessary to configure the calculator so that what is entered or this output corresponds to radians or degrees.

To configure the calculator you must locate the function for it. In many, the mode (RAD or DEG) is defined or there is a selection between the two modes:

image

GRDs do not correspond to degrees, it is a decimal measure in which the 90 degree angle is defined as 100.

Pythagoras

The relationship between a and b and the hypotenuse c satisfies according to Pythagoras

equation

Sum of angles

Two angles \alpha and \beta can be added together giving a third angle \gamma

equation

Sine

The relationship between the angle \theta, the opposite leg b and the hypotenuse c is given by the relationship

equation

To calculate the corresponding function can be used

image

Cosine

The relationship between the angle \theta, the adjacent leg a and the hypotenuse c is given by the relationship

equation

To calculate the corresponding function can be used

image

Tangent

The relationship between the angle \theta, the adjacent leg a and opposite b is given by the relation

equation

To calculate the corresponding function can be used

image

Cotangent

The relationship between the angle \theta, the adjacent leg a and opposite b is given by the relation

equation

The cotangent is the inverse function to the tangent function.

Tangent Ratio

The tangent function is written according to the cosine and the sine by:

equation

Relationship between Cosine and Sine

Pythagoras obtains the relationship between the cosine and the sine of an angle

equation

Arcsinus

The angle \theta is obtained from the opposite leg b and the hypotenuse c through the relation

equation

The \arcsin function is the inverse function of \sin.

To calculate the corresponding function can be used

image

Arc Cosine

The angle \theta is obtained from the adjacent leg a and the hypotenuse c through the relation

equation

The \arccos function is the inverse function of \cos.

To calculate the corresponding function can be used

image

Arc Tangent

The angle \theta is obtained from the opposite leg b and the adjacent leg a by means of the relation

equation

The \arctan function is the inverse function of \tan.

To calculate the corresponding function can be used

image

Arco Cotangent

The angle \theta is obtained from the opposite leg b and the adjacent leg a by means of the relation

equation

The \mathrm{arccot} function is the inverse function of \cot.

Sine of the Sum

The sine of the sum of two angles can be written according to the cosine and sine of the individual angles:

equation

Cosine of the Sum

The cosine of the sum of two angles can be written according to the cosine and sine of the individual angles:

equation

Tangent of the Sum

The tangent of the sum of two angles can be written according to the cosine and sine of the individual angles:

equation

>Model

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