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Popolare Trigonometria >

sin(110-x/2)=-sin(70)

Soluzione

sin (11 0^{\circ} - \frac{x}{2}) = - sin (7 0^{\circ})

Soluzione

x = - 72 0^{\circ} n + 22 0^{\circ} - 2 (- 1.22173 \dots), x = - 36 0^{\circ} - 72 0^{\circ} n + 8 0^{\circ}

Radianti

x = \frac{11 π}{9} - 2 (- 1.22173 \dots) - 4 πn, x = - 2 π + \frac{4 π}{9} - 4 πn

Fasi della soluzione

sin (11 0^{\circ} - \frac{x}{2}) = - sin (7 0^{\circ})

Applica le proprietà inverse delle funzioni trigonometriche

sin (11 0^{\circ} - \frac{x}{2}) = - sin (7 0^{\circ})

Soluzioni generali per

sin (11 0^{\circ} - \frac{x}{2}) = - sin (7 0^{\circ})

sin (x) = - a \Rightarrow x = arcsin (- a) + 36 0^{\circ} n, x = 18 0^{\circ} + arcsin (a) + 36 0^{\circ} n

11 0^{\circ} - \frac{x}{2} = arcsin (- sin (7 0^{\circ})) + 36 0^{\circ} n, 11 0^{\circ} - \frac{x}{2} = 18 0^{\circ} + arcsin (sin (7 0^{\circ})) + 36 0^{\circ} n

11 0^{\circ} - \frac{x}{2} = arcsin (- sin (7 0^{\circ})) + 36 0^{\circ} n, 11 0^{\circ} - \frac{x}{2} = 18 0^{\circ} + arcsin (sin (7 0^{\circ})) + 36 0^{\circ} n

Risolvi

11 0^{\circ} - \frac{x}{2} = arcsin (- sin (7 0^{\circ})) + 36 0^{\circ} n : x = - 72 0^{\circ} n + 22 0^{\circ} - 2 arcsin (- sin (7 0^{\circ}))

11 0^{\circ} - \frac{x}{2} = arcsin (- sin (7 0^{\circ})) + 36 0^{\circ} n

Spostare

11 0^{\circ}

a destra dell'equazione

11 0^{\circ} - \frac{x}{2} = arcsin (- sin (7 0^{\circ})) + 36 0^{\circ} n

Sottrarre

11 0^{\circ}

da entrambi i lati

11 0^{\circ} - \frac{x}{2} - 11 0^{\circ} = arcsin (- sin (7 0^{\circ})) + 36 0^{\circ} n - 11 0^{\circ}

Semplificare

- \frac{x}{2} = arcsin (- sin (7 0^{\circ})) + 36 0^{\circ} n - 11 0^{\circ}

- \frac{x}{2} = arcsin (- sin (7 0^{\circ})) + 36 0^{\circ} n - 11 0^{\circ}

Moltiplica entrambi i lati per

2

- \frac{x}{2} = arcsin (- sin (7 0^{\circ})) + 36 0^{\circ} n - 11 0^{\circ}

Moltiplica entrambi i lati per

2

2 (- \frac{x}{2}) = 2 arcsin (- sin (7 0^{\circ})) + 2 \cdot 36 0^{\circ} n - 2 \cdot 11 0^{\circ}

Semplificare

2 (- \frac{x}{2}) = 2 arcsin (- sin (7 0^{\circ})) + 2 \cdot 36 0^{\circ} n - 2 \cdot 11 0^{\circ}

Semplificare

2 (- \frac{x}{2}) : - x

2 (- \frac{x}{2})

Rimuovi le parentesi:

(- a) = - a

= - 2 \cdot \frac{x}{2}

Moltiplica le frazioni:

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

= - \frac{x \cdot 2}{2}

Cancella il fattore comune:

2

= - x

Semplificare

2 arcsin (- sin (7 0^{\circ})) + 2 \cdot 36 0^{\circ} n - 2 \cdot 11 0^{\circ} : 2 arcsin (- sin (7 0^{\circ})) + 72 0^{\circ} n - 22 0^{\circ}

2 arcsin (- sin (7 0^{\circ})) + 2 \cdot 36 0^{\circ} n - 2 \cdot 11 0^{\circ}

2 \cdot 36 0^{\circ} n = 72 0^{\circ} n

2 \cdot 36 0^{\circ} n

Moltiplica i numeri:

2 \cdot 2 = 4

= 72 0^{\circ} n

2 \cdot 11 0^{\circ} = 22 0^{\circ}

2 \cdot 11 0^{\circ}

Moltiplica le frazioni:

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

= 22 0^{\circ}

Moltiplica i numeri:

11 \cdot 2 = 22

= 22 0^{\circ}

Cancella il fattore comune:

2

= 22 0^{\circ}

= 2 arcsin (- sin (7 0^{\circ})) + 72 0^{\circ} n - 22 0^{\circ}

- x = 2 arcsin (- sin (7 0^{\circ})) + 72 0^{\circ} n - 22 0^{\circ}

- x = 2 arcsin (- sin (7 0^{\circ})) + 72 0^{\circ} n - 22 0^{\circ}

- x = 2 arcsin (- sin (7 0^{\circ})) + 72 0^{\circ} n - 22 0^{\circ}

Dividere entrambi i lati per

- 1

- x = 2 arcsin (- sin (7 0^{\circ})) + 72 0^{\circ} n - 22 0^{\circ}

Dividere entrambi i lati per

- 1

\frac{- x}{- 1} = \frac{2 arcsin ( - sin ( 7 0 ^{\circ} ) )}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{22 0 ^{\circ}}{- 1}

Semplificare

\frac{- x}{- 1} = \frac{2 arcsin ( - sin ( 7 0 ^{\circ} ) )}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{22 0 ^{\circ}}{- 1}

Semplificare

\frac{- x}{- 1} : x

\frac{- x}{- 1}

Applica la regola delle frazioni:

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

= \frac{x}{1}

Applicare la regola

\frac{a}{1} = a

= x

Semplificare

\frac{2 arcsin ( - sin ( 7 0 ^{\circ} ) )}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{22 0 ^{\circ}}{- 1} : - 72 0^{\circ} n + 22 0^{\circ} - 2 arcsin (- sin (7 0^{\circ}))

\frac{2 arcsin ( - sin ( 7 0 ^{\circ} ) )}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{22 0 ^{\circ}}{- 1}

Raggruppa termini simili

= \frac{72 0 ^{\circ} n}{- 1} - \frac{22 0 ^{\circ}}{- 1} + \frac{2 arcsin ( - sin ( 7 0 ^{\circ} ) )}{- 1}

\frac{72 0 ^{\circ} n}{- 1} = - 72 0^{\circ} n

\frac{72 0 ^{\circ} n}{- 1}

Applica la regola delle frazioni:

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

= - \frac{72 0 ^{\circ} n}{1}

Applicare la regola

\frac{a}{1} = a

= - 72 0^{\circ} n

= - 72 0^{\circ} n - \frac{22 0 ^{\circ}}{- 1} + \frac{2 arcsin ( - sin ( 7 0 ^{\circ} ) )}{- 1}

\frac{22 0 ^{\circ}}{- 1} = - 22 0^{\circ}

\frac{22 0 ^{\circ}}{- 1}

Applica la regola delle frazioni:

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

= - \frac{22 0 ^{\circ}}{1}

Applica la regola delle frazioni:

\frac{a}{1} = a

\frac{22 0 ^{\circ}}{1} = 22 0^{\circ}

= - 22 0^{\circ}

\frac{2 arcsin ( - sin ( 7 0 ^{\circ} ) )}{- 1} = - 2 arcsin (- sin (7 0^{\circ}))

\frac{2 arcsin ( - sin ( 7 0 ^{\circ} ) )}{- 1}

Applica la regola delle frazioni:

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

= - \frac{2 arcsin ( - sin ( 7 0 ^{\circ} ) )}{1}

Applica la regola delle frazioni:

\frac{a}{1} = a

\frac{2 arcsin ( - sin ( 7 0 ^{\circ} ) )}{1} = 2 arcsin (- sin (7 0^{\circ}))

= - 2 arcsin (- sin (7 0^{\circ}))

= - 72 0^{\circ} n - (- 22 0^{\circ}) - 2 arcsin (- sin (7 0^{\circ}))

Applicare la regola

- (- a) = a

= - 72 0^{\circ} n + 22 0^{\circ} - 2 arcsin (- sin (7 0^{\circ}))

x = - 72 0^{\circ} n + 22 0^{\circ} - 2 arcsin (- sin (7 0^{\circ}))

x = - 72 0^{\circ} n + 22 0^{\circ} - 2 arcsin (- sin (7 0^{\circ}))

x = - 72 0^{\circ} n + 22 0^{\circ} - 2 arcsin (- sin (7 0^{\circ}))

Risolvi

11 0^{\circ} - \frac{x}{2} = 18 0^{\circ} + arcsin (sin (7 0^{\circ})) + 36 0^{\circ} n : x = - 36 0^{\circ} - 72 0^{\circ} n + 8 0^{\circ}

11 0^{\circ} - \frac{x}{2} = 18 0^{\circ} + arcsin (sin (7 0^{\circ})) + 36 0^{\circ} n

arcsin (sin (7 0^{\circ})) = 7 0^{\circ}

arcsin (sin (7 0^{\circ}))

Per

- 9 0^{\circ} \leq x \leq 9 0^{\circ}, a rcs in (s in (x)) = x

- 9 0^{\circ} \leq 7 0^{\circ} \leq 9 0^{\circ}

= 7 0^{\circ}

11 0^{\circ} - \frac{x}{2} = 18 0^{\circ} + 7 0^{\circ} + 36 0^{\circ} n

Spostare

11 0^{\circ}

a destra dell'equazione

11 0^{\circ} - \frac{x}{2} = 18 0^{\circ} + 7 0^{\circ} + 36 0^{\circ} n

Sottrarre

11 0^{\circ}

da entrambi i lati

11 0^{\circ} - \frac{x}{2} - 11 0^{\circ} = 18 0^{\circ} + 7 0^{\circ} + 36 0^{\circ} n - 11 0^{\circ}

Semplificare

11 0^{\circ} - \frac{x}{2} - 11 0^{\circ} = 18 0^{\circ} + 7 0^{\circ} + 36 0^{\circ} n - 11 0^{\circ}

Semplificare

11 0^{\circ} - \frac{x}{2} - 11 0^{\circ} : - \frac{x}{2}

11 0^{\circ} - \frac{x}{2} - 11 0^{\circ}

Aggiungi elementi simili:

11 0^{\circ} - 11 0^{\circ} = 0

= - \frac{x}{2}

Semplificare

18 0^{\circ} + 7 0^{\circ} + 36 0^{\circ} n - 11 0^{\circ} : 18 0^{\circ} + 36 0^{\circ} n - 4 0^{\circ}

18 0^{\circ} + 7 0^{\circ} + 36 0^{\circ} n - 11 0^{\circ}

Raggruppa termini simili

= 18 0^{\circ} + 36 0^{\circ} n + 7 0^{\circ} - 11 0^{\circ}

Combinare le frazioni

7 0^{\circ} - 11 0^{\circ} : - 4 0^{\circ}

Applicare la regola

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

= \frac{126 0 ^{\circ} - 198 0 ^{\circ}}{18}

Aggiungi elementi simili:

126 0^{\circ} - 198 0^{\circ} = - 72 0^{\circ}

= \frac{- 72 0 ^{\circ}}{18}

Applica la regola delle frazioni:

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

= - 4 0^{\circ}

Cancella il fattore comune:

2

= - 4 0^{\circ}

= 18 0^{\circ} + 36 0^{\circ} n - 4 0^{\circ}

- \frac{x}{2} = 18 0^{\circ} + 36 0^{\circ} n - 4 0^{\circ}

- \frac{x}{2} = 18 0^{\circ} + 36 0^{\circ} n - 4 0^{\circ}

- \frac{x}{2} = 18 0^{\circ} + 36 0^{\circ} n - 4 0^{\circ}

Moltiplica entrambi i lati per

2

- \frac{x}{2} = 18 0^{\circ} + 36 0^{\circ} n - 4 0^{\circ}

Moltiplica entrambi i lati per

2

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

Semplificare

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

Semplificare

2 (- \frac{x}{2}) : - x

2 (- \frac{x}{2})

Rimuovi le parentesi:

(- a) = - a

= - 2 \cdot \frac{x}{2}

Moltiplica le frazioni:

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

= - \frac{x \cdot 2}{2}

Cancella il fattore comune:

2

= - x

Semplificare

36 0^{\circ} + 2 \cdot 36 0^{\circ} n - 2 \cdot 4 0^{\circ} : 36 0^{\circ} + 72 0^{\circ} n - 8 0^{\circ}

36 0^{\circ} + 2 \cdot 36 0^{\circ} n - 2 \cdot 4 0^{\circ}

2 \cdot 36 0^{\circ} n = 72 0^{\circ} n

2 \cdot 36 0^{\circ} n

Moltiplica i numeri:

2 \cdot 2 = 4

= 72 0^{\circ} n

2 \cdot 4 0^{\circ} = 8 0^{\circ}

2 \cdot 4 0^{\circ}

Moltiplica le frazioni:

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

= 8 0^{\circ}

Moltiplica i numeri:

2 \cdot 2 = 4

= 8 0^{\circ}

= 36 0^{\circ} + 72 0^{\circ} n - 8 0^{\circ}

- x = 36 0^{\circ} + 72 0^{\circ} n - 8 0^{\circ}

- x = 36 0^{\circ} + 72 0^{\circ} n - 8 0^{\circ}

- x = 36 0^{\circ} + 72 0^{\circ} n - 8 0^{\circ}

Dividere entrambi i lati per

- 1

- x = 36 0^{\circ} + 72 0^{\circ} n - 8 0^{\circ}

Dividere entrambi i lati per

- 1

\frac{- x}{- 1} = \frac{36 0 ^{\circ}}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{8 0 ^{\circ}}{- 1}

Semplificare

\frac{- x}{- 1} = \frac{36 0 ^{\circ}}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{8 0 ^{\circ}}{- 1}

Semplificare

\frac{- x}{- 1} : x

\frac{- x}{- 1}

Applica la regola delle frazioni:

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

= \frac{x}{1}

Applicare la regola

\frac{a}{1} = a

= x

Semplificare

\frac{36 0 ^{\circ}}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{8 0 ^{\circ}}{- 1} : - 36 0^{\circ} - 72 0^{\circ} n + 8 0^{\circ}

\frac{36 0 ^{\circ}}{- 1} + \frac{72 0 ^{\circ} n}{- 1} - \frac{8 0 ^{\circ}}{- 1}

\frac{36 0 ^{\circ}}{- 1} = - 36 0^{\circ}

\frac{36 0 ^{\circ}}{- 1}

Applica la regola delle frazioni:

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

= - 36 0^{\circ}

Applicare la regola

\frac{a}{1} = a

= - 36 0^{\circ}

= - 36 0^{\circ} + \frac{72 0 ^{\circ} n}{- 1} - \frac{8 0 ^{\circ}}{- 1}

\frac{72 0 ^{\circ} n}{- 1} = - 72 0^{\circ} n

\frac{72 0 ^{\circ} n}{- 1}

Applica la regola delle frazioni:

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

= - \frac{72 0 ^{\circ} n}{1}

Applicare la regola

\frac{a}{1} = a

= - 72 0^{\circ} n

= - 36 0^{\circ} - 72 0^{\circ} n - \frac{8 0 ^{\circ}}{- 1}

\frac{8 0 ^{\circ}}{- 1} = - 8 0^{\circ}

\frac{8 0 ^{\circ}}{- 1}

Applica la regola delle frazioni:

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

= - \frac{8 0 ^{\circ}}{1}

Applica la regola delle frazioni:

\frac{a}{1} = a

\frac{8 0 ^{\circ}}{1} = 8 0^{\circ}

= - 8 0^{\circ}

= - 36 0^{\circ} - 72 0^{\circ} n - (- 8 0^{\circ})

Applicare la regola

- (- a) = a

= - 36 0^{\circ} - 72 0^{\circ} n + 8 0^{\circ}

x = - 36 0^{\circ} - 72 0^{\circ} n + 8 0^{\circ}

x = - 36 0^{\circ} - 72 0^{\circ} n + 8 0^{\circ}

x = - 36 0^{\circ} - 72 0^{\circ} n + 8 0^{\circ}

x = - 72 0^{\circ} n + 22 0^{\circ} - 2 arcsin (- sin (7 0^{\circ})), x = - 36 0^{\circ} - 72 0^{\circ} n + 8 0^{\circ}

Mostra le soluzioni in forma decimale

x = - 72 0^{\circ} n + 22 0^{\circ} - 2 (- 1.22173 \dots), x = - 36 0^{\circ} - 72 0^{\circ} n + 8 0^{\circ}

Grafico

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