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Popolare Trigonometria >

cos(180-x)=sin(-300)

Soluzione

cos (18 0^{\circ} - x) = sin (- 30 0^{\circ})

Soluzione

x = 18 0^{\circ} - 36 0^{\circ} n - 3 0^{\circ}, x = 18 0^{\circ} - 36 0^{\circ} n - 33 0^{\circ}

Radianti

x = π - \frac{π}{6} - 2 πn, x = π - \frac{11 π}{6} - 2 πn

Fasi della soluzione

cos (18 0^{\circ} - x) = sin (- 30 0^{\circ})

sin (- 30 0^{\circ}) = \frac{3}{2}

sin (- 30 0^{\circ})

Usare la proprietà seguente:

sin (- x) = - sin (x)

sin (- 30 0^{\circ}) = - sin (30 0^{\circ})

= - sin (30 0^{\circ})

Riscrivere utilizzando identità trigonometriche:

sin (30 0^{\circ}) = - \frac{3}{2}

sin (30 0^{\circ})

Riscrivere utilizzando identità trigonometriche:

sin (18 0^{\circ}) cos (12 0^{\circ}) + cos (18 0^{\circ}) sin (12 0^{\circ})

sin (30 0^{\circ})

Scrivere

sin (30 0^{\circ})

come

sin (18 0^{\circ} + 12 0^{\circ})

= sin (18 0^{\circ} + 12 0^{\circ})

Usa la formula della somma degli angoli:

sin (s + t) = sin (s) cos (t) + cos (s) sin (t)

= sin (18 0^{\circ}) cos (12 0^{\circ}) + cos (18 0^{\circ}) sin (12 0^{\circ})

= sin (18 0^{\circ}) cos (12 0^{\circ}) + cos (18 0^{\circ}) sin (12 0^{\circ})

Usare la seguente identità triviale:

sin (18 0^{\circ}) = 0

sin (18 0^{\circ})

sin (x)

periodicità tabella con

36 0^{\circ} n

cicli:

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}

= 0

Usare la seguente identità triviale:

cos (12 0^{\circ}) = - \frac{1}{2}

cos (12 0^{\circ})

cos (x)

periodicità tabella con

36 0^{\circ} n

cicli:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= - \frac{1}{2}

Usare la seguente identità triviale:

cos (18 0^{\circ}) = (- 1)

cos (18 0^{\circ})

cos (x)

periodicità tabella con

36 0^{\circ} n

cicli:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= (- 1)

Usare la seguente identità triviale:

sin (12 0^{\circ}) = \frac{3}{2}

sin (12 0^{\circ})

sin (x)

periodicità tabella con

36 0^{\circ} n

cicli:

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{3}{2}

= 0 \cdot (- \frac{1}{2}) + (- 1) \frac{3}{2}

Semplificare

= - \frac{3}{2}

= - (- \frac{3}{2})

Semplificare

= \frac{3}{2}

cos (18 0^{\circ} - x) = \frac{3}{2}

Soluzioni generali per

cos (18 0^{\circ} - x) = \frac{3}{2}

cos (x)

periodicità tabella con

36 0^{\circ} n

cicli:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

18 0^{\circ} - x = 3 0^{\circ} + 36 0^{\circ} n, 18 0^{\circ} - x = 33 0^{\circ} + 36 0^{\circ} n

18 0^{\circ} - x = 3 0^{\circ} + 36 0^{\circ} n, 18 0^{\circ} - x = 33 0^{\circ} + 36 0^{\circ} n

Risolvi

18 0^{\circ} - x = 3 0^{\circ} + 36 0^{\circ} n : x = 18 0^{\circ} - 36 0^{\circ} n - 3 0^{\circ}

18 0^{\circ} - x = 3 0^{\circ} + 36 0^{\circ} n

Spostare

18 0^{\circ}

a destra dell'equazione

18 0^{\circ} - x = 3 0^{\circ} + 36 0^{\circ} n

Sottrarre

18 0^{\circ}

da entrambi i lati

18 0^{\circ} - x - 18 0^{\circ} = 3 0^{\circ} + 36 0^{\circ} n - 18 0^{\circ}

Semplificare

- x = 3 0^{\circ} + 36 0^{\circ} n - 18 0^{\circ}

- x = 3 0^{\circ} + 36 0^{\circ} n - 18 0^{\circ}

Dividere entrambi i lati per

- 1

- x = 3 0^{\circ} + 36 0^{\circ} n - 18 0^{\circ}

Dividere entrambi i lati per

- 1

\frac{- x}{- 1} = \frac{3 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{18 0 ^{\circ}}{- 1}

Semplificare

\frac{- x}{- 1} = \frac{3 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{18 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{3 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{18 0 ^{\circ}}{- 1} : 18 0^{\circ} - 36 0^{\circ} n - 3 0^{\circ}

\frac{3 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{18 0 ^{\circ}}{- 1}

Raggruppa termini simili

= - \frac{18 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} + \frac{3 0 ^{\circ}}{- 1}

\frac{18 0 ^{\circ}}{- 1} = - 18 0^{\circ}

\frac{18 0 ^{\circ}}{- 1}

Applica la regola delle frazioni:

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

= - 18 0^{\circ}

Applicare la regola

\frac{a}{1} = a

= - 18 0^{\circ}

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

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

Applica la regola delle frazioni:

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

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

Applicare la regola

\frac{a}{1} = a

= - 36 0^{\circ} n

= - (- 18 0^{\circ}) - 36 0^{\circ} n + \frac{3 0 ^{\circ}}{- 1}

Applicare la regola

- (- a) = a

= 18 0^{\circ} - 36 0^{\circ} n + \frac{3 0 ^{\circ}}{- 1}

\frac{3 0 ^{\circ}}{- 1} = - 3 0^{\circ}

\frac{3 0 ^{\circ}}{- 1}

Applica la regola delle frazioni:

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

= - \frac{3 0 ^{\circ}}{1}

Applica la regola delle frazioni:

\frac{a}{1} = a

\frac{3 0 ^{\circ}}{1} = 3 0^{\circ}

= - 3 0^{\circ}

= 18 0^{\circ} - 36 0^{\circ} n - 3 0^{\circ}

x = 18 0^{\circ} - 36 0^{\circ} n - 3 0^{\circ}

x = 18 0^{\circ} - 36 0^{\circ} n - 3 0^{\circ}

x = 18 0^{\circ} - 36 0^{\circ} n - 3 0^{\circ}

Risolvi

18 0^{\circ} - x = 33 0^{\circ} + 36 0^{\circ} n : x = 18 0^{\circ} - 36 0^{\circ} n - 33 0^{\circ}

18 0^{\circ} - x = 33 0^{\circ} + 36 0^{\circ} n

Spostare

18 0^{\circ}

a destra dell'equazione

18 0^{\circ} - x = 33 0^{\circ} + 36 0^{\circ} n

Sottrarre

18 0^{\circ}

da entrambi i lati

18 0^{\circ} - x - 18 0^{\circ} = 33 0^{\circ} + 36 0^{\circ} n - 18 0^{\circ}

Semplificare

- x = 33 0^{\circ} + 36 0^{\circ} n - 18 0^{\circ}

- x = 33 0^{\circ} + 36 0^{\circ} n - 18 0^{\circ}

Dividere entrambi i lati per

- 1

- x = 33 0^{\circ} + 36 0^{\circ} n - 18 0^{\circ}

Dividere entrambi i lati per

- 1

\frac{- x}{- 1} = \frac{33 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{18 0 ^{\circ}}{- 1}

Semplificare

\frac{- x}{- 1} = \frac{33 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{18 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{33 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{18 0 ^{\circ}}{- 1} : 18 0^{\circ} - 36 0^{\circ} n - 33 0^{\circ}

\frac{33 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{18 0 ^{\circ}}{- 1}

Raggruppa termini simili

= - \frac{18 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} + \frac{33 0 ^{\circ}}{- 1}

\frac{18 0 ^{\circ}}{- 1} = - 18 0^{\circ}

\frac{18 0 ^{\circ}}{- 1}

Applica la regola delle frazioni:

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

= - 18 0^{\circ}

Applicare la regola

\frac{a}{1} = a

= - 18 0^{\circ}

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

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

Applica la regola delle frazioni:

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

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

Applicare la regola

\frac{a}{1} = a

= - 36 0^{\circ} n

= - (- 18 0^{\circ}) - 36 0^{\circ} n + \frac{33 0 ^{\circ}}{- 1}

Applicare la regola

- (- a) = a

= 18 0^{\circ} - 36 0^{\circ} n + \frac{33 0 ^{\circ}}{- 1}

\frac{33 0 ^{\circ}}{- 1} = - 33 0^{\circ}

\frac{33 0 ^{\circ}}{- 1}

Applica la regola delle frazioni:

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

= - \frac{33 0 ^{\circ}}{1}

Applica la regola delle frazioni:

\frac{a}{1} = a

\frac{33 0 ^{\circ}}{1} = 33 0^{\circ}

= - 33 0^{\circ}

= 18 0^{\circ} - 36 0^{\circ} n - 33 0^{\circ}

x = 18 0^{\circ} - 36 0^{\circ} n - 33 0^{\circ}

x = 18 0^{\circ} - 36 0^{\circ} n - 33 0^{\circ}

x = 18 0^{\circ} - 36 0^{\circ} n - 33 0^{\circ}

x = 18 0^{\circ} - 36 0^{\circ} n - 3 0^{\circ}, x = 18 0^{\circ} - 36 0^{\circ} n - 33 0^{\circ}

Grafico

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