English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometria >

cos(x/4)sin(x/4)=sqrt(3)sin(x/4)cos(x/4)

Solução

cos (\frac{x}{4}) sin (\frac{x}{4}) = 3 sin (\frac{x}{4}) cos (\frac{x}{4})

Solução

x = 2 π + 8 πn, x = 6 π + 8 πn, x = 8 πn, x = 4 π + 8 πn

Graus

x = 36 0^{\circ} + 144 0^{\circ} n, x = 108 0^{\circ} + 144 0^{\circ} n, x = 0^{\circ} + 144 0^{\circ} n, x = 72 0^{\circ} + 144 0^{\circ} n

Passos da solução

cos (\frac{x}{4}) sin (\frac{x}{4}) = 3 sin (\frac{x}{4}) cos (\frac{x}{4})

Subtrair

3 sin (\frac{x}{4}) cos (\frac{x}{4})

de ambos os lados

cos (\frac{x}{4}) sin (\frac{x}{4}) - 3 sin (\frac{x}{4}) cos (\frac{x}{4}) = 0

Fatorar

cos (\frac{x}{4}) sin (\frac{x}{4}) - 3 sin (\frac{x}{4}) cos (\frac{x}{4}) : (1 - 3) cos (\frac{x}{4}) sin (\frac{x}{4})

cos (\frac{x}{4}) sin (\frac{x}{4}) - 3 sin (\frac{x}{4}) cos (\frac{x}{4})

Fatorar o termo comum

cos (\frac{x}{4}) sin (\frac{x}{4})

= cos (\frac{x}{4}) sin (\frac{x}{4}) (1 - 3)

(1 - 3) cos (\frac{x}{4}) sin (\frac{x}{4}) = 0

Resolver cada parte separadamente

cos (\frac{x}{4}) = 0 or sin (\frac{x}{4}) = 0

cos (\frac{x}{4}) = 0 : x = 2 π + 8 πn, x = 6 π + 8 πn

cos (\frac{x}{4}) = 0

Soluções gerais para

cos (\frac{x}{4}) = 0

cos (x)

tabela de periodicidade com ciclo de

2 πn

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

\frac{x}{4} = \frac{π}{2} + 2 πn, \frac{x}{4} = \frac{3 π}{2} + 2 πn

\frac{x}{4} = \frac{π}{2} + 2 πn, \frac{x}{4} = \frac{3 π}{2} + 2 πn

Resolver

\frac{x}{4} = \frac{π}{2} + 2 πn : x = 2 π + 8 πn

\frac{x}{4} = \frac{π}{2} + 2 πn

Multiplicar ambos os lados por

4

\frac{x}{4} = \frac{π}{2} + 2 πn

Multiplicar ambos os lados por

4

\frac{4 x}{4} = 4 \cdot \frac{π}{2} + 4 \cdot 2 πn

Simplificar

\frac{4 x}{4} = 4 \cdot \frac{π}{2} + 4 \cdot 2 πn

Simplificar

\frac{4 x}{4} : x

\frac{4 x}{4}

Dividir:

\frac{4}{4} = 1

= x

Simplificar

4 \cdot \frac{π}{2} + 4 \cdot 2 πn : 2 π + 8 πn

4 \cdot \frac{π}{2} + 4 \cdot 2 πn

4 \cdot \frac{π}{2} = 2 π

4 \cdot \frac{π}{2}

Multiplicar frações:

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

= \frac{π 4}{2}

Dividir:

\frac{4}{2} = 2

= 2 π

4 \cdot 2 πn = 8 πn

4 \cdot 2 πn

Multiplicar os números:

4 \cdot 2 = 8

= 8 πn

= 2 π + 8 πn

x = 2 π + 8 πn

x = 2 π + 8 πn

x = 2 π + 8 πn

Resolver

\frac{x}{4} = \frac{3 π}{2} + 2 πn : x = 6 π + 8 πn

\frac{x}{4} = \frac{3 π}{2} + 2 πn

Multiplicar ambos os lados por

4

\frac{x}{4} = \frac{3 π}{2} + 2 πn

Multiplicar ambos os lados por

4

\frac{4 x}{4} = 4 \cdot \frac{3 π}{2} + 4 \cdot 2 πn

Simplificar

\frac{4 x}{4} = 4 \cdot \frac{3 π}{2} + 4 \cdot 2 πn

Simplificar

\frac{4 x}{4} : x

\frac{4 x}{4}

Dividir:

\frac{4}{4} = 1

= x

Simplificar

4 \cdot \frac{3 π}{2} + 4 \cdot 2 πn : 6 π + 8 πn

4 \cdot \frac{3 π}{2} + 4 \cdot 2 πn

4 \cdot \frac{3 π}{2} = 6 π

4 \cdot \frac{3 π}{2}

Multiplicar frações:

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

= \frac{3 π 4}{2}

Multiplicar os números:

3 \cdot 4 = 12

= \frac{12 π}{2}

Dividir:

\frac{12}{2} = 6

= 6 π

4 \cdot 2 πn = 8 πn

4 \cdot 2 πn

Multiplicar os números:

4 \cdot 2 = 8

= 8 πn

= 6 π + 8 πn

x = 6 π + 8 πn

x = 6 π + 8 πn

x = 6 π + 8 πn

x = 2 π + 8 πn, x = 6 π + 8 πn

sin (\frac{x}{4}) = 0 : x = 8 πn, x = 4 π + 8 πn

sin (\frac{x}{4}) = 0

Soluções gerais para

sin (\frac{x}{4}) = 0

sin (x)

tabela de periodicidade com ciclo de

2 πn

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{x}{4} = 0 + 2 πn, \frac{x}{4} = π + 2 πn

\frac{x}{4} = 0 + 2 πn, \frac{x}{4} = π + 2 πn

Resolver

\frac{x}{4} = 0 + 2 πn : x = 8 πn

\frac{x}{4} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{x}{4} = 2 πn

Multiplicar ambos os lados por

4

\frac{x}{4} = 2 πn

Multiplicar ambos os lados por

4

\frac{4 x}{4} = 4 \cdot 2 πn

Simplificar

x = 8 πn

x = 8 πn

Resolver

\frac{x}{4} = π + 2 πn : x = 4 π + 8 πn

\frac{x}{4} = π + 2 πn

Multiplicar ambos os lados por

4

\frac{x}{4} = π + 2 πn

Multiplicar ambos os lados por

4

\frac{4 x}{4} = 4 π + 4 \cdot 2 πn

Simplificar

x = 4 π + 8 πn

x = 4 π + 8 πn

x = 8 πn, x = 4 π + 8 πn

Combinar toda as soluções

x = 2 π + 8 πn, x = 6 π + 8 πn, x = 8 πn, x = 4 π + 8 πn

Gráfico

Exemplos populares

5cos(x)=1+2sin^2(x)

5 cos (x) = 1 + 2 sin^{2} (x)

tan(2x+1)=-cot(x+3)

tan (2 x + 1) = - cot (x + 3)

(4sec^2(x))/2 =-8sec(x)

\frac{4 sec ^{2} ( x )}{2} = - 8 sec (x)

tan(x)+tan^3(x)=0

tan (x) + tan^{3} (x) = 0

sin^3(x)-2sin(x)=4cos^2(x)-3

sin^{3} (x) - 2 sin (x) = 4 cos^{2} (x) - 3