English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popolare Trigonometria >

cos(3x)=(sqrt(3))/3

Soluzione

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

Soluzione

x = \frac{0.95531 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{0.95531 \dots}{3} + \frac{2 πn}{3}

Gradi

x = 18.24520 \dots^{\circ} + 12 0^{\circ} n, x = 101.75479 \dots^{\circ} + 12 0^{\circ} n

Fasi della soluzione

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

Applica le proprietà inverse delle funzioni trigonometriche

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

Soluzioni generali per

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

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

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

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

Risolvi

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

3 x = arccos (\frac{3}{3}) + 2 πn

Semplificare

arccos (\frac{3}{3}) + 2 πn : arccos (\frac{1}{3}) + 2 πn

arccos (\frac{3}{3}) + 2 πn

\frac{3}{3} = \frac{1}{3}

\frac{3}{3}

Applicare la regola della radice:

n a = a^{\frac{1}{n}}

3 = 3^{\frac{1}{2}}

= \frac{3 ^{\frac{1}{2}}}{3}

Applica la regola degli esponenti:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{3 ^{\frac{1}{2}}}{3 ^{1}} = \frac{1}{3 ^{1 - \frac{1}{2}}}

= \frac{1}{3 ^{1 - \frac{1}{2}}}

Sottrai i numeri:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{1}{3 ^{\frac{1}{2}}}

Applicare la regola della radice:

a^{\frac{1}{n}} = n a

3^{\frac{1}{2}} = 3

= \frac{1}{3}

= arccos (\frac{1}{3}) + 2 πn

3 x = arccos (\frac{1}{3}) + 2 πn

Dividere entrambi i lati per

3

3 x = arccos (\frac{1}{3}) + 2 πn

Dividere entrambi i lati per

3

\frac{3 x}{3} = \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

Semplificare

\frac{3 x}{3} = \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

Semplificare

\frac{3 x}{3} : x

\frac{3 x}{3}

Dividi i numeri:

\frac{3}{3} = 1

= x

Semplificare

\frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3} : \frac{arccos ( \frac{3}{3} )}{3} + \frac{2 πn}{3}

\frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

arccos (\frac{1}{3}) = arccos (\frac{3}{3})

arccos (\frac{1}{3})

= arccos (\frac{3}{3})

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

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

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

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

Risolvi

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

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

Semplificare

2 π - arccos (\frac{3}{3}) + 2 πn : 2 π - arccos (\frac{1}{3}) + 2 πn

2 π - arccos (\frac{3}{3}) + 2 πn

\frac{3}{3} = \frac{1}{3}

\frac{3}{3}

Applicare la regola della radice:

n a = a^{\frac{1}{n}}

3 = 3^{\frac{1}{2}}

= \frac{3 ^{\frac{1}{2}}}{3}

Applica la regola degli esponenti:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{3 ^{\frac{1}{2}}}{3 ^{1}} = \frac{1}{3 ^{1 - \frac{1}{2}}}

= \frac{1}{3 ^{1 - \frac{1}{2}}}

Sottrai i numeri:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{1}{3 ^{\frac{1}{2}}}

Applicare la regola della radice:

a^{\frac{1}{n}} = n a

3^{\frac{1}{2}} = 3

= \frac{1}{3}

= 2 π - arccos (\frac{1}{3}) + 2 πn

3 x = 2 π - arccos (\frac{1}{3}) + 2 πn

Dividere entrambi i lati per

3

3 x = 2 π - arccos (\frac{1}{3}) + 2 πn

Dividere entrambi i lati per

3

\frac{3 x}{3} = \frac{2 π}{3} - \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

Semplificare

\frac{3 x}{3} = \frac{2 π}{3} - \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

Semplificare

\frac{3 x}{3} : x

\frac{3 x}{3}

Dividi i numeri:

\frac{3}{3} = 1

= x

Semplificare

\frac{2 π}{3} - \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3} : \frac{2 π}{3} - \frac{arccos ( \frac{3}{3} )}{3} + \frac{2 πn}{3}

\frac{2 π}{3} - \frac{arccos ( \frac{1}{3} )}{3} + \frac{2 πn}{3}

arccos (\frac{1}{3}) = arccos (\frac{3}{3})

arccos (\frac{1}{3})

= arccos (\frac{3}{3})

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

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

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

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

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

Mostra le soluzioni in forma decimale

x = \frac{0.95531 \dots}{3} + \frac{2 πn}{3}, x = \frac{2 π}{3} - \frac{0.95531 \dots}{3} + \frac{2 πn}{3}

Grafico

Esempi popolari

-6csc^2(x)+cot(x)=-18

- 6 csc^{2} (x) + cot (x) = - 18

tan(θ)= 7/7

tan (θ) = \frac{7}{7}

tan(2x)=0.75

tan (2 x) = 0.75

3tan^2(x)+7tan(x)+4=0

3 tan^{2} (x) + 7 tan (x) + 4 = 0

cos(2θ)-3=-5sin(θ)

cos (2 θ) - 3 = - 5 sin (θ)