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Popolare Trigonometria >

cos(5a+40)= 3/5

Soluzione

cos (5 a + 4 0^{\circ}) = \frac{3}{5}

Soluzione

a = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{0.92729 \dots}{5}, a = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{0.92729 \dots}{5}

Radianti

a = - \frac{2 π}{45} + \frac{0.92729 \dots}{5} + \frac{2 π}{5} n, a = \frac{2 π}{5} - \frac{2 π}{45} - \frac{0.92729 \dots}{5} + \frac{2 π}{5} n

Fasi della soluzione

cos (5 a + 4 0^{\circ}) = \frac{3}{5}

Applica le proprietà inverse delle funzioni trigonometriche

cos (5 a + 4 0^{\circ}) = \frac{3}{5}

Soluzioni generali per

cos (5 a + 4 0^{\circ}) = \frac{3}{5}

cos (x) = a \Rightarrow x = arccos (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (a) + 36 0^{\circ} n

5 a + 4 0^{\circ} = arccos (\frac{3}{5}) + 36 0^{\circ} n, 5 a + 4 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n

5 a + 4 0^{\circ} = arccos (\frac{3}{5}) + 36 0^{\circ} n, 5 a + 4 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n

Risolvi

5 a + 4 0^{\circ} = arccos (\frac{3}{5}) + 36 0^{\circ} n : a = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

5 a + 4 0^{\circ} = arccos (\frac{3}{5}) + 36 0^{\circ} n

Spostare

4 0^{\circ}

a destra dell'equazione

5 a + 4 0^{\circ} = arccos (\frac{3}{5}) + 36 0^{\circ} n

Sottrarre

4 0^{\circ}

da entrambi i lati

5 a + 4 0^{\circ} - 4 0^{\circ} = arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

Semplificare

5 a = arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

5 a = arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

Dividere entrambi i lati per

5

5 a = arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

Dividere entrambi i lati per

5

\frac{5 a}{5} = \frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5}

Semplificare

\frac{5 a}{5} = \frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5}

Semplificare

\frac{5 a}{5} : a

\frac{5 a}{5}

Dividi i numeri:

\frac{5}{5} = 1

= a

Semplificare

\frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5} : \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

\frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5}

Raggruppa termini simili

= \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5} + \frac{arccos ( \frac{3}{5} )}{5}

\frac{4 0 ^{\circ}}{5} = 8^{\circ}

\frac{4 0 ^{\circ}}{5}

Applica la regola delle frazioni:

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

= \frac{36 0 ^{\circ}}{9 \cdot 5}

Moltiplica i numeri:

9 \cdot 5 = 45

= 8^{\circ}

= \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

a = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

a = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

a = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

Risolvi

5 a + 4 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n : a = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

5 a + 4 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n

Spostare

4 0^{\circ}

a destra dell'equazione

5 a + 4 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n

Sottrarre

4 0^{\circ}

da entrambi i lati

5 a + 4 0^{\circ} - 4 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

Semplificare

5 a = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

5 a = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

Dividere entrambi i lati per

5

5 a = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

Dividere entrambi i lati per

5

\frac{5 a}{5} = 7 2^{\circ} - \frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5}

Semplificare

\frac{5 a}{5} = 7 2^{\circ} - \frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5}

Semplificare

\frac{5 a}{5} : a

\frac{5 a}{5}

Dividi i numeri:

\frac{5}{5} = 1

= a

Semplificare

7 2^{\circ} - \frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5} : 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

7 2^{\circ} - \frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5}

Raggruppa termini simili

= 7 2^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5} - \frac{arccos ( \frac{3}{5} )}{5}

\frac{4 0 ^{\circ}}{5} = 8^{\circ}

\frac{4 0 ^{\circ}}{5}

Applica la regola delle frazioni:

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

= \frac{36 0 ^{\circ}}{9 \cdot 5}

Moltiplica i numeri:

9 \cdot 5 = 45

= 8^{\circ}

= 7 2^{\circ} + \frac{36 0 ^{\circ} n}{5} - 8^{\circ} - \frac{arccos ( \frac{3}{5} )}{5}

Raggruppa termini simili

= 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

a = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

a = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

a = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

a = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}, a = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

Mostra le soluzioni in forma decimale

a = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{0.92729 \dots}{5}, a = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{0.92729 \dots}{5}

Grafico

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