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Popular Trigonometría >

tan(x-20)=tan(2x+10)

Solución

tan (x - 2 0^{\circ}) = tan (2 x + 10)

Solución

x = - 36 0^{\circ} n - 2 0^{\circ} - 10, x = - 10 - 20 0^{\circ} - 36 0^{\circ} n

Radianes

x = - \frac{π}{9} - 10 - 2 πn, x = - 10 - \frac{10 π}{9} - 2 πn

Pasos de solución

tan (x - 2 0^{\circ}) = tan (2 x + 10)

Restar

tan (2 x + 10)

de ambos lados

tan (x - 2 0^{\circ}) - tan (2 x + 10) = 0

Expresar con seno, coseno

tan (- 2 0^{\circ} + x) - tan (10 + 2 x)

Utilizar la identidad trigonométrica básica:

tan (x) = \frac{sin ( x )}{cos ( x )}

= \frac{sin ( - 2 0 ^{\circ} + x )}{cos ( - 2 0 ^{\circ} + x )} - tan (10 + 2 x)

Utilizar la identidad trigonométrica básica:

tan (x) = \frac{sin ( x )}{cos ( x )}

= \frac{sin ( - 2 0 ^{\circ} + x )}{cos ( - 2 0 ^{\circ} + x )} - \frac{sin ( 10 + 2 x )}{cos ( 10 + 2 x )}

Simplificar

\frac{sin ( - 2 0 ^{\circ} + x )}{cos ( - 2 0 ^{\circ} + x )} - \frac{sin ( 10 + 2 x )}{cos ( 10 + 2 x )} : \frac{sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) cos ( 2 x + 10 ) - sin ( 10 + 2 x ) cos ( \frac{9 x - 18 0 ^{\circ}}{9} )}{cos ( \frac{9 x - 18 0 ^{\circ}}{9} ) cos ( 2 x + 10 )}

\frac{sin ( - 2 0 ^{\circ} + x )}{cos ( - 2 0 ^{\circ} + x )} - \frac{sin ( 10 + 2 x )}{cos ( 10 + 2 x )}

\frac{sin ( - 2 0 ^{\circ} + x )}{cos ( - 2 0 ^{\circ} + x )} = \frac{sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} )}{cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} )}

\frac{sin ( - 2 0 ^{\circ} + x )}{cos ( - 2 0 ^{\circ} + x )}

Simplificar

- 2 0^{\circ} + x

en una fracción:

\frac{- 18 0 ^{\circ} + 9 x}{9}

- 2 0^{\circ} + x

Convertir a fracción:

x = \frac{x 9}{9}

= - 2 0^{\circ} + \frac{x \cdot 9}{9}

Ya que los denominadores son iguales, combinar las fracciones:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- 18 0 ^{\circ} + x \cdot 9}{9}

= \frac{sin ( - 2 0 ^{\circ} + x )}{cos ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} )}

Simplificar

- 2 0^{\circ} + x

en una fracción:

\frac{- 18 0 ^{\circ} + 9 x}{9}

- 2 0^{\circ} + x

Convertir a fracción:

x = \frac{x 9}{9}

= - 2 0^{\circ} + \frac{x \cdot 9}{9}

Ya que los denominadores son iguales, combinar las fracciones:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- 18 0 ^{\circ} + x \cdot 9}{9}

= \frac{sin ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} )}{cos ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} )}

= \frac{sin ( \frac{9 x - 18 0 ^{\circ}}{9} )}{cos ( \frac{9 x - 18 0 ^{\circ}}{9} )} - \frac{sin ( 2 x + 10 )}{cos ( 2 x + 10 )}

Mínimo común múltiplo de

cos (\frac{- 18 0 ^{\circ} + x 9}{9}), cos (10 + 2 x) : cos (\frac{9 x - 18 0 ^{\circ}}{9}) cos (2 x + 10)

cos (\frac{- 18 0 ^{\circ} + x \cdot 9}{9}), cos (10 + 2 x)

Mínimo común múltiplo (MCM)

Calcular una expresión que este compuesta de factores que aparezcan tanto en

cos (\frac{- 18 0 ^{\circ} + x 9}{9})

cos (10 + 2 x)

= cos (\frac{9 x - 18 0 ^{\circ}}{9}) cos (2 x + 10)

Reescribir las fracciones basandose en el mínimo común denominador

Multiplicar cada numerador por la misma cantidad necesaria para multiplicar el denominador correspondiente y convertirlo en el mínimo común denominador

Para

\frac{sin ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} )}{cos ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} )} :

multiplicar el denominador y el numerador por

cos (2 x + 10)

\frac{sin ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} )}{cos ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} )} = \frac{sin ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} ) cos ( 2 x + 10 )}{cos ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} ) cos ( 2 x + 10 )}

Para

\frac{sin ( 10 + 2 x )}{cos ( 10 + 2 x )} :

multiplicar el denominador y el numerador por

cos (\frac{9 x - 18 0 ^{\circ}}{9})

\frac{sin ( 10 + 2 x )}{cos ( 10 + 2 x )} = \frac{sin ( 10 + 2 x ) cos ( \frac{9 x - 18 0 ^{\circ}}{9} )}{cos ( 10 + 2 x ) cos ( \frac{9 x - 18 0 ^{\circ}}{9} )}

= \frac{sin ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} ) cos ( 2 x + 10 )}{cos ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} ) cos ( 2 x + 10 )} - \frac{sin ( 10 + 2 x ) cos ( \frac{9 x - 18 0 ^{\circ}}{9} )}{cos ( 10 + 2 x ) cos ( \frac{9 x - 18 0 ^{\circ}}{9} )}

Ya que los denominadores son iguales, combinar las fracciones:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{sin ( \frac{- 18 0 ^{\circ} + x \cdot 9}{9} ) cos ( 2 x + 10 ) - sin ( 10 + 2 x ) cos ( \frac{9 x - 18 0 ^{\circ}}{9} )}{cos ( \frac{9 x - 18 0 ^{\circ}}{9} ) cos ( 2 x + 10 )}

= \frac{sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) cos ( 2 x + 10 ) - sin ( 10 + 2 x ) cos ( \frac{9 x - 18 0 ^{\circ}}{9} )}{cos ( \frac{9 x - 18 0 ^{\circ}}{9} ) cos ( 2 x + 10 )}

\frac{cos ( 10 + 2 x ) sin ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) - cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} ) sin ( 10 + 2 x )}{cos ( 10 + 2 x ) cos ( \frac{- 18 0 ^{\circ} + 9 x}{9} )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

cos (10 + 2 x) sin (\frac{- 18 0 ^{\circ} + 9 x}{9}) - cos (\frac{- 18 0 ^{\circ} + 9 x}{9}) sin (10 + 2 x) = 0

Re-escribir usando identidades trigonométricas

cos (10 + 2 x) sin (\frac{- 18 0 ^{\circ} + 9 x}{9}) - cos (\frac{- 18 0 ^{\circ} + 9 x}{9}) sin (10 + 2 x)

Utilizar la identidad de diferencia de ángulos:

sin (s) cos (t) - cos (s) sin (t) = sin (s - t)

= sin (\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x))

sin (\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x)) = 0

Soluciones generales para

sin (\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x)) = 0

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x) = 0 + 36 0^{\circ} n, \frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x) = 18 0^{\circ} + 36 0^{\circ} n

\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x) = 0 + 36 0^{\circ} n, \frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x) = 18 0^{\circ} + 36 0^{\circ} n

Resolver

\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x) = 0 + 36 0^{\circ} n : x = - 36 0^{\circ} n - 2 0^{\circ} - 10

\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x) = 0 + 36 0^{\circ} n

0 + 36 0^{\circ} n = 36 0^{\circ} n

\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x) = 36 0^{\circ} n

Multiplicar ambos lados por

9

\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x) = 36 0^{\circ} n

Multiplicar ambos lados por

9

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 9 - (10 + 2 x) \cdot 9 = 36 0^{\circ} n \cdot 9

Simplificar

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 9 - (10 + 2 x) \cdot 9 = 36 0^{\circ} n \cdot 9

Simplificar

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 9 : - 18 0^{\circ} + 9 x

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 9

Multiplicar fracciones:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( - 18 0 ^{\circ} + 9 x ) \cdot 9}{9}

Eliminar los terminos comunes:

9

= - - 18 0^{\circ} + 9 x

Simplificar

(10 + 2 x) \cdot 9 : 9 (10 + 2 x)

(10 + 2 x) \cdot 9

Aplica la ley conmutativa:

(10 + 2 x) \cdot 9 = 9 (10 + 2 x)

9 (10 + 2 x)

Simplificar

36 0^{\circ} n \cdot 9 : 324 0^{\circ} n

36 0^{\circ} n \cdot 9

Multiplicar los numeros:

2 \cdot 9 = 18

= 324 0^{\circ} n

- 18 0^{\circ} + 9 x - 9 (10 + 2 x) = 324 0^{\circ} n

- 18 0^{\circ} + 9 x - 9 (10 + 2 x) = 324 0^{\circ} n

- 18 0^{\circ} + 9 x - 9 (10 + 2 x) = 324 0^{\circ} n

Desarrollar

- 18 0^{\circ} + 9 x - 9 (10 + 2 x) : - 9 x - 18 0^{\circ} - 90

- 18 0^{\circ} + 9 x - 9 (10 + 2 x)

Expandir

- 9 (10 + 2 x) : - 90 - 18 x

- 9 (10 + 2 x)

Poner los parentesis utilizando:

a (b + c) = ab + a c

a = - 9, b = 10, c = 2 x

= - 9 \cdot 10 + (- 9) \cdot 2 x

Aplicar las reglas de los signos

+ (- a) = - a

= - 9 \cdot 10 - 9 \cdot 2 x

Simplificar

- 9 \cdot 10 - 9 \cdot 2 x : - 90 - 18 x

- 9 \cdot 10 - 9 \cdot 2 x

Multiplicar los numeros:

9 \cdot 10 = 90

= - 90 - 9 \cdot 2 x

Multiplicar los numeros:

9 \cdot 2 = 18

= - 90 - 18 x

= - 90 - 18 x

= - 18 0^{\circ} + 9 x - 90 - 18 x

Simplificar

- 18 0^{\circ} + 9 x - 90 - 18 x : - 9 x - 18 0^{\circ} - 90

- 18 0^{\circ} + 9 x - 90 - 18 x

Agrupar términos semejantes

= 9 x - 18 x - 18 0^{\circ} - 90

Sumar elementos similares:

9 x - 18 x = - 9 x

= - 9 x - 18 0^{\circ} - 90

= - 9 x - 18 0^{\circ} - 90

- 9 x - 18 0^{\circ} - 90 = 324 0^{\circ} n

Desplace

18 0^{\circ}

a la derecha

- 9 x - 18 0^{\circ} - 90 = 324 0^{\circ} n

Sumar

18 0^{\circ}

a ambos lados

- 9 x - 18 0^{\circ} - 90 + 18 0^{\circ} = 324 0^{\circ} n + 18 0^{\circ}

Simplificar

- 9 x - 90 = 324 0^{\circ} n + 18 0^{\circ}

- 9 x - 90 = 324 0^{\circ} n + 18 0^{\circ}

Desplace

90

a la derecha

- 9 x - 90 = 324 0^{\circ} n + 18 0^{\circ}

Sumar

90

a ambos lados

- 9 x - 90 + 90 = 324 0^{\circ} n + 18 0^{\circ} + 90

Simplificar

- 9 x = 324 0^{\circ} n + 18 0^{\circ} + 90

- 9 x = 324 0^{\circ} n + 18 0^{\circ} + 90

Dividir ambos lados entre

- 9

- 9 x = 324 0^{\circ} n + 18 0^{\circ} + 90

Dividir ambos lados entre

- 9

\frac{- 9 x}{- 9} = \frac{324 0 ^{\circ} n}{- 9} + \frac{18 0 ^{\circ}}{- 9} + \frac{90}{- 9}

Simplificar

\frac{- 9 x}{- 9} = \frac{324 0 ^{\circ} n}{- 9} + \frac{18 0 ^{\circ}}{- 9} + \frac{90}{- 9}

Simplificar

\frac{- 9 x}{- 9} : x

\frac{- 9 x}{- 9}

Aplicar las propiedades de las fracciones:

\frac{- a}{- b} = \frac{a}{b}

= \frac{9 x}{9}

Dividir:

\frac{9}{9} = 1

= x

Simplificar

\frac{324 0 ^{\circ} n}{- 9} + \frac{18 0 ^{\circ}}{- 9} + \frac{90}{- 9} : - 36 0^{\circ} n - 2 0^{\circ} - 10

\frac{324 0 ^{\circ} n}{- 9} + \frac{18 0 ^{\circ}}{- 9} + \frac{90}{- 9}

\frac{324 0 ^{\circ} n}{- 9} = - 36 0^{\circ} n

\frac{324 0 ^{\circ} n}{- 9}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{324 0 ^{\circ} n}{9}

Dividir:

\frac{18}{9} = 2

= - 36 0^{\circ} n

= - 36 0^{\circ} n + \frac{18 0 ^{\circ}}{- 9} + \frac{90}{- 9}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - 36 0^{\circ} n - 2 0^{\circ} + \frac{90}{- 9}

\frac{90}{- 9} = - 10

\frac{90}{- 9}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{90}{9}

Dividir:

\frac{90}{9} = 10

= - 10

= - 36 0^{\circ} n - 2 0^{\circ} - 10

x = - 36 0^{\circ} n - 2 0^{\circ} - 10

x = - 36 0^{\circ} n - 2 0^{\circ} - 10

x = - 36 0^{\circ} n - 2 0^{\circ} - 10

Resolver

\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x) = 18 0^{\circ} + 36 0^{\circ} n : x = - 10 - 20 0^{\circ} - 36 0^{\circ} n

\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x) = 18 0^{\circ} + 36 0^{\circ} n

Multiplicar ambos lados por

9

\frac{- 18 0 ^{\circ} + 9 x}{9} - (10 + 2 x) = 18 0^{\circ} + 36 0^{\circ} n

Multiplicar ambos lados por

9

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 9 - (10 + 2 x) \cdot 9 = 18 0^{\circ} 9 + 36 0^{\circ} n \cdot 9

Simplificar

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 9 - (10 + 2 x) \cdot 9 = 18 0^{\circ} 9 + 36 0^{\circ} n \cdot 9

Simplificar

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 9 : - 18 0^{\circ} + 9 x

\frac{- 18 0 ^{\circ} + 9 x}{9} \cdot 9

Multiplicar fracciones:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{( - 18 0 ^{\circ} + 9 x ) \cdot 9}{9}

Eliminar los terminos comunes:

9

= - - 18 0^{\circ} + 9 x

Simplificar

(10 + 2 x) \cdot 9 : 9 (10 + 2 x)

(10 + 2 x) \cdot 9

Aplica la ley conmutativa:

(10 + 2 x) \cdot 9 = 9 (10 + 2 x)

9 (10 + 2 x)

Simplificar

18 0^{\circ} 9 : 162 0^{\circ}

18 0^{\circ} 9

Aplica la ley conmutativa:

18 0^{\circ} 9 = 162 0^{\circ}

162 0^{\circ}

Simplificar

36 0^{\circ} n \cdot 9 : 324 0^{\circ} n

36 0^{\circ} n \cdot 9

Multiplicar los numeros:

2 \cdot 9 = 18

= 324 0^{\circ} n

- 18 0^{\circ} + 9 x - 9 (10 + 2 x) = 162 0^{\circ} + 324 0^{\circ} n

- 18 0^{\circ} + 9 x - 9 (10 + 2 x) = 162 0^{\circ} + 324 0^{\circ} n

- 18 0^{\circ} + 9 x - 9 (10 + 2 x) = 162 0^{\circ} + 324 0^{\circ} n

Desarrollar

- 18 0^{\circ} + 9 x - 9 (10 + 2 x) : - 9 x - 18 0^{\circ} - 90

- 18 0^{\circ} + 9 x - 9 (10 + 2 x)

Expandir

- 9 (10 + 2 x) : - 90 - 18 x

- 9 (10 + 2 x)

Poner los parentesis utilizando:

a (b + c) = ab + a c

a = - 9, b = 10, c = 2 x

= - 9 \cdot 10 + (- 9) \cdot 2 x

Aplicar las reglas de los signos

+ (- a) = - a

= - 9 \cdot 10 - 9 \cdot 2 x

Simplificar

- 9 \cdot 10 - 9 \cdot 2 x : - 90 - 18 x

- 9 \cdot 10 - 9 \cdot 2 x

Multiplicar los numeros:

9 \cdot 10 = 90

= - 90 - 9 \cdot 2 x

Multiplicar los numeros:

9 \cdot 2 = 18

= - 90 - 18 x

= - 90 - 18 x

= - 18 0^{\circ} + 9 x - 90 - 18 x

Simplificar

- 18 0^{\circ} + 9 x - 90 - 18 x : - 9 x - 18 0^{\circ} - 90

- 18 0^{\circ} + 9 x - 90 - 18 x

Agrupar términos semejantes

= 9 x - 18 x - 18 0^{\circ} - 90

Sumar elementos similares:

9 x - 18 x = - 9 x

= - 9 x - 18 0^{\circ} - 90

= - 9 x - 18 0^{\circ} - 90

- 9 x - 18 0^{\circ} - 90 = 162 0^{\circ} + 324 0^{\circ} n

Desplace

18 0^{\circ}

a la derecha

- 9 x - 18 0^{\circ} - 90 = 162 0^{\circ} + 324 0^{\circ} n

Sumar

18 0^{\circ}

a ambos lados

- 9 x - 18 0^{\circ} - 90 + 18 0^{\circ} = 162 0^{\circ} + 324 0^{\circ} n + 18 0^{\circ}

Simplificar

- 9 x - 90 = 180 0^{\circ} + 324 0^{\circ} n

- 9 x - 90 = 180 0^{\circ} + 324 0^{\circ} n

Desplace

90

a la derecha

- 9 x - 90 = 180 0^{\circ} + 324 0^{\circ} n

Sumar

90

a ambos lados

- 9 x - 90 + 90 = 180 0^{\circ} + 324 0^{\circ} n + 90

Simplificar

- 9 x = 180 0^{\circ} + 324 0^{\circ} n + 90

- 9 x = 180 0^{\circ} + 324 0^{\circ} n + 90

Dividir ambos lados entre

- 9

- 9 x = 180 0^{\circ} + 324 0^{\circ} n + 90

Dividir ambos lados entre

- 9

\frac{- 9 x}{- 9} = \frac{180 0 ^{\circ}}{- 9} + \frac{324 0 ^{\circ} n}{- 9} + \frac{90}{- 9}

Simplificar

\frac{- 9 x}{- 9} = \frac{180 0 ^{\circ}}{- 9} + \frac{324 0 ^{\circ} n}{- 9} + \frac{90}{- 9}

Simplificar

\frac{- 9 x}{- 9} : x

\frac{- 9 x}{- 9}

Aplicar las propiedades de las fracciones:

\frac{- a}{- b} = \frac{a}{b}

= \frac{9 x}{9}

Dividir:

\frac{9}{9} = 1

= x

Simplificar

\frac{180 0 ^{\circ}}{- 9} + \frac{324 0 ^{\circ} n}{- 9} + \frac{90}{- 9} : - 10 - 20 0^{\circ} - 36 0^{\circ} n

\frac{180 0 ^{\circ}}{- 9} + \frac{324 0 ^{\circ} n}{- 9} + \frac{90}{- 9}

Agrupar términos semejantes

= \frac{90}{- 9} + \frac{180 0 ^{\circ}}{- 9} + \frac{324 0 ^{\circ} n}{- 9}

\frac{90}{- 9} = - 10

\frac{90}{- 9}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{90}{9}

Dividir:

\frac{90}{9} = 10

= - 10

= - 10 + \frac{180 0 ^{\circ}}{- 9} + \frac{324 0 ^{\circ} n}{- 9}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - 10 - 20 0^{\circ} + \frac{324 0 ^{\circ} n}{- 9}

\frac{324 0 ^{\circ} n}{- 9} = - 36 0^{\circ} n

\frac{324 0 ^{\circ} n}{- 9}

Aplicar las propiedades de las fracciones:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{324 0 ^{\circ} n}{9}

Dividir:

\frac{18}{9} = 2

= - 36 0^{\circ} n

= - 10 - 20 0^{\circ} - 36 0^{\circ} n

x = - 10 - 20 0^{\circ} - 36 0^{\circ} n

x = - 10 - 20 0^{\circ} - 36 0^{\circ} n

x = - 10 - 20 0^{\circ} - 36 0^{\circ} n

x = - 36 0^{\circ} n - 2 0^{\circ} - 10, x = - 10 - 20 0^{\circ} - 36 0^{\circ} n

Gráfica

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