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7cos(3x)=2,0<= x<2pi

Soluzione

7 cos (3 x) = 2, 0 \leq x < 2 π

x = \frac{1.28104 \dots}{3}, x = \frac{2 π - 1.28104 \dots}{3}, x = \frac{1.28104 \dots + 2 π}{3}, x = \frac{4 π - 1.28104 \dots}{3}, x = \frac{1.28104 \dots + 4 π}{3}, x = \frac{6 π - 1.28104 \dots}{3}

Gradi

x = 24.46615 \dots^{\circ}, x = 95.53384 \dots^{\circ}, x = 144.46615 \dots^{\circ}, x = 215.53384 \dots^{\circ}, x = 264.46615 \dots^{\circ}, x = 335.53384 \dots^{\circ}

Fasi della soluzione

7 cos (3 x) = 2, 0 \leq x < 2 π

Dividere entrambi i lati per

7

7 cos (3 x) = 2

Dividere entrambi i lati per

7

\frac{7 cos ( 3 x )}{7} = \frac{2}{7}

Semplificare

cos (3 x) = \frac{2}{7}

cos (3 x) = \frac{2}{7}

Applica le proprietà inverse delle funzioni trigonometriche

cos (3 x) = \frac{2}{7}

Soluzioni generali per

cos (3 x) = \frac{2}{7}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

3 x = arccos (\frac{2}{7}) + 2 πn, 3 x = 2 π - arccos (\frac{2}{7}) + 2 πn

3 x = arccos (\frac{2}{7}) + 2 πn, 3 x = 2 π - arccos (\frac{2}{7}) + 2 πn

Risolvi

3 x = arccos (\frac{2}{7}) + 2 πn : x = \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

3 x = arccos (\frac{2}{7}) + 2 πn

Dividere entrambi i lati per

3

3 x = arccos (\frac{2}{7}) + 2 πn

Dividere entrambi i lati per

3

\frac{3 x}{3} = \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

Semplificare

x = \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

Risolvi

3 x = 2 π - arccos (\frac{2}{7}) + 2 πn : x = \frac{2 π}{3} - \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

3 x = 2 π - arccos (\frac{2}{7}) + 2 πn

Dividere entrambi i lati per

3

3 x = 2 π - arccos (\frac{2}{7}) + 2 πn

Dividere entrambi i lati per

3

\frac{3 x}{3} = \frac{2 π}{3} - \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

Semplificare

x = \frac{2 π}{3} - \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

x = \frac{2 π}{3} - \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

x = \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{arccos ( \frac{2}{7} )}{3} + \frac{2 πn}{3}

Soluzioni per l'intervallo

0 \leq x < 2 π

x = \frac{arccos ( \frac{2}{7} )}{3}, x = \frac{2 π - arccos ( \frac{2}{7} )}{3}, x = \frac{arccos ( \frac{2}{7} ) + 2 π}{3}, x = \frac{4 π - arccos ( \frac{2}{7} )}{3}, x = \frac{arccos ( \frac{2}{7} ) + 4 π}{3}, x = \frac{6 π - arccos ( \frac{2}{7} )}{3}

Mostra le soluzioni in forma decimale

x = \frac{1.28104 \dots}{3}, x = \frac{2 π - 1.28104 \dots}{3}, x = \frac{1.28104 \dots + 2 π}{3}, x = \frac{4 π - 1.28104 \dots}{3}, x = \frac{1.28104 \dots + 4 π}{3}, x = \frac{6 π - 1.28104 \dots}{3}

6 cos (2 x) = 3

arctan (\frac{x}{42}) = 57

3 tan^{2} (x) = 19

3.6 = 0.116 cos (4.17 x)

cos (x) = \frac{3}{2}, sin (2 x), - 9 0^{\circ} \leq x \leq 0^{\circ}