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Trigonometric Functions
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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.

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

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Trigonometric functions
Description

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



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

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Calculation in radians and degrees
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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:



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

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Pythagoras
Equation

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

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

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Sum of angles
Equation

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

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

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Sine
Equation

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

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



To calculate the corresponding function can be used

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Cosine
Equation

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

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



To calculate the corresponding function can be used

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Tangent
Equation

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

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



To calculate the corresponding function can be used

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Cotangent
Equation

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

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

The cotangent is the inverse function to the tangent function.

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Tangent Ratio
Equation

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

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

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Relationship between Cosine and Sine
Equation

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

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

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Arcsinus
Equation

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

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



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

To calculate the corresponding function can be used

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Arc Cosine
Equation

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

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



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

To calculate the corresponding function can be used

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Arc Tangent
Equation

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

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



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

To calculate the corresponding function can be used

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Arco Cotangent
Equation

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

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

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

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Sine of the Sum
Equation

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

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

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Cosine of the Sum
Equation

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

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

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Tangent of the Sum
Equation

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

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

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