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Popular Trigonometría >

270=69-tan(45+(x/2))

Solución

270 = 69 - tan (4 5^{\circ} + (\frac{x}{2}))

Solución

x = - 2 \cdot 1.56582 \dots + 36 0^{\circ} n - 9 0^{\circ}

+1

Radianes

x = - 2 \cdot 1.56582 \dots - \frac{π}{2} + 2 πn

Pasos de solución

270 = 69 - tan (4 5^{\circ} + (\frac{x}{2}))

Intercambiar lados

69 - tan (4 5^{\circ} + \frac{x}{2}) = 270

Desplace

69

a la derecha

69 - tan (4 5^{\circ} + \frac{x}{2}) = 270

Restar

69

de ambos lados

69 - tan (4 5^{\circ} + \frac{x}{2}) - 69 = 270 - 69

Simplificar

- tan (4 5^{\circ} + \frac{x}{2}) = 201

- tan (4 5^{\circ} + \frac{x}{2}) = 201

Dividir ambos lados entre

- 1

- tan (4 5^{\circ} + \frac{x}{2}) = 201

Dividir ambos lados entre

- 1

\frac{- tan ( 4 5 ^{\circ} + \frac{x}{2} )}{- 1} = \frac{201}{- 1}

Simplificar

tan (4 5^{\circ} + \frac{x}{2}) = - 201

tan (4 5^{\circ} + \frac{x}{2}) = - 201

Aplicar propiedades trigonométricas inversas

tan (4 5^{\circ} + \frac{x}{2}) = - 201

Soluciones generales para

tan (4 5^{\circ} + \frac{x}{2}) = - 201

tan (x) = - a \Rightarrow x = arctan (- a) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = arctan (- 201) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = arctan (- 201) + 18 0^{\circ} n

Resolver

4 5^{\circ} + \frac{x}{2} = arctan (- 201) + 18 0^{\circ} n : x = - 2 arctan (201) + 36 0^{\circ} n - 9 0^{\circ}

4 5^{\circ} + \frac{x}{2} = arctan (- 201) + 18 0^{\circ} n

Simplificar

arctan (- 201) + 18 0^{\circ} n : - arctan (201) + 18 0^{\circ} n

arctan (- 201) + 18 0^{\circ} n

Utilizar la siguiente propiedad:

arctan (- x) = - arctan (x)

arctan (- 201) = - arctan (201)

= - arctan (201) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = - arctan (201) + 18 0^{\circ} n

Desplace

4 5^{\circ}

a la derecha

4 5^{\circ} + \frac{x}{2} = - arctan (201) + 18 0^{\circ} n

Restar

4 5^{\circ}

de ambos lados

4 5^{\circ} + \frac{x}{2} - 4 5^{\circ} = - arctan (201) + 18 0^{\circ} n - 4 5^{\circ}

Simplificar

\frac{x}{2} = - arctan (201) + 18 0^{\circ} n - 4 5^{\circ}

\frac{x}{2} = - arctan (201) + 18 0^{\circ} n - 4 5^{\circ}

Multiplicar ambos lados por

2

\frac{x}{2} = - arctan (201) + 18 0^{\circ} n - 4 5^{\circ}

Multiplicar ambos lados por

2

\frac{2 x}{2} = - 2 arctan (201) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

Simplificar

\frac{2 x}{2} = - 2 arctan (201) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

Simplificar

\frac{2 x}{2} : x

\frac{2 x}{2}

Dividir:

\frac{2}{2} = 1

= x

Simplificar

- 2 arctan (201) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ} : - 2 arctan (201) + 36 0^{\circ} n - 9 0^{\circ}

- 2 arctan (201) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

2 \cdot 4 5^{\circ} = 9 0^{\circ}

2 \cdot 4 5^{\circ}

Multiplicar fracciones:

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

= 9 0^{\circ}

Eliminar los terminos comunes:

2

= 9 0^{\circ}

= - 2 arctan (201) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (201) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (201) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (201) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (201) + 36 0^{\circ} n - 9 0^{\circ}

Mostrar soluciones en forma decimal

x = - 2 \cdot 1.56582 \dots + 36 0^{\circ} n - 9 0^{\circ}

Gráfica

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