English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometria >

cos(x-45)< 1/2 ,0<= x<= 360

Solução

cos (x - 4 5^{\circ}) < \frac{1}{2}, 0^{\circ} \leq x \leq 36 0^{\circ}

Solução

\frac{π + 3 \cdot 4 5 ^{\circ}}{3} < x < \frac{5 π + 3 \cdot 4 5 ^{\circ}}{3}

Notação de intervalo

(\frac{π + 34 5 ^{\circ}}{3}, \frac{5 π + 34 5 ^{\circ}}{3})

Decimal

1.83259 \dots < x < 6.02138 \dots

Passos da solução

cos (x - 4 5^{\circ}) < \frac{1}{2}, 0^{\circ} \leq x \leq 36 0^{\circ}

Para

cos (x) < a

, se

- 1 < a \leq 1

então

arccos (a) + 2 πn < x < 2 π - arccos (a) + 2 πn

arccos (\frac{1}{2}) + 2 πn < (x - 4 5^{\circ}) < 2 π - arccos (\frac{1}{2}) + 2 πn

a < u < b

então

a < u and u < b

arccos (\frac{1}{2}) + 2 πn < x - 4 5^{\circ} and x - 4 5^{\circ} < 2 π - arccos (\frac{1}{2}) + 2 πn

arccos (\frac{1}{2}) + 2 πn < x - 4 5^{\circ} : x > \frac{π + 3 \cdot 4 5 ^{\circ}}{3} + 2 πn

arccos (\frac{1}{2}) + 2 πn < x - 4 5^{\circ}

Trocar lados

x - 4 5^{\circ} > arccos (\frac{1}{2}) + 2 πn

Simplificar

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

arccos (\frac{1}{2}) + 2 πn

Utilizar a seguinte identidade trivial:

arccos (\frac{1}{2}) = \frac{π}{3}

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= \frac{π}{3} + 2 πn

x - 4 5^{\circ} > \frac{π}{3} + 2 πn

Mova

4 5^{\circ}

para o lado direito

x - 4 5^{\circ} > \frac{π}{3} + 2 πn

Adicionar

4 5^{\circ}

a ambos os lados

x - 4 5^{\circ} + 4 5^{\circ} > \frac{π}{3} + 2 πn + 4 5^{\circ}

Simplificar

x > \frac{π}{3} + 2 πn + 4 5^{\circ}

x > \frac{π}{3} + 2 πn + 4 5^{\circ}

Simplificar

\frac{π}{3} + 4 5^{\circ} : \frac{π + 3 \cdot 4 5 ^{\circ}}{3}

\frac{π}{3} + 4 5^{\circ}

Converter para fração:

4 5^{\circ} = \frac{4 5 ^{\circ} \cdot 3}{3}

= \frac{π}{3} + \frac{4 5 ^{\circ} \cdot 3}{3}

Já que os denominadores são iguais, combinar as frações:

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

= \frac{π + 4 5 ^{\circ} \cdot 3}{3}

x > \frac{π + 3 \cdot 4 5 ^{\circ}}{3} + 2 πn

x - 4 5^{\circ} < 2 π - arccos (\frac{1}{2}) + 2 πn : x < \frac{5 π + 3 \cdot 4 5 ^{\circ}}{3} + 2 πn

x - 4 5^{\circ} < 2 π - arccos (\frac{1}{2}) + 2 πn

Simplificar

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

2 π - arccos (\frac{1}{2}) + 2 πn

Utilizar a seguinte identidade trivial:

arccos (\frac{1}{2}) = \frac{π}{3}

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= 2 π - \frac{π}{3} + 2 πn

x - 4 5^{\circ} < 2 π - \frac{π}{3} + 2 πn

Mova

4 5^{\circ}

para o lado direito

x - 4 5^{\circ} < 2 π - \frac{π}{3} + 2 πn

Adicionar

4 5^{\circ}

a ambos os lados

x - 4 5^{\circ} + 4 5^{\circ} < 2 π - \frac{π}{3} + 2 πn + 4 5^{\circ}

Simplificar

x < 2 π - \frac{π}{3} + 2 πn + 4 5^{\circ}

x < 2 π - \frac{π}{3} + 2 πn + 4 5^{\circ}

Simplificar

2 π - \frac{π}{3} + 4 5^{\circ} : \frac{5 π + 3 \cdot 4 5 ^{\circ}}{3}

2 π - \frac{π}{3} + 4 5^{\circ}

Converter para fração:

2 π = \frac{2 π 3}{3}, 4 5^{\circ} = \frac{4 5 ^{\circ} \cdot 3}{3}

= \frac{2 π 3}{3} - \frac{π}{3} + \frac{4 5 ^{\circ} \cdot 3}{3}

Já que os denominadores são iguais, combinar as frações:

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

= \frac{2 π 3 - π + 4 5 ^{\circ} \cdot 3}{3}

2 π 3 - π + 4 5^{\circ} \cdot 3 = 5 π + 3 \cdot 4 5^{\circ}

2 π 3 - π + 4 5^{\circ} \cdot 3

Multiplicar os números:

2 \cdot 3 = 6

= 6 π - π + 3 \cdot 4 5^{\circ}

Somar elementos similares:

6 π - π = 5 π

= 5 π + 3 \cdot 4 5^{\circ}

= \frac{5 π + 3 \cdot 4 5 ^{\circ}}{3}

x < \frac{5 π + 3 \cdot 4 5 ^{\circ}}{3} + 2 πn

Combinar os intervalos

x > \frac{π + 3 \cdot 4 5 ^{\circ}}{3} + 2 πn and x < \frac{5 π + 3 \cdot 4 5 ^{\circ}}{3} + 2 πn

Junte intervalos que se sobrepoem

\frac{π + 3 \cdot 4 5 ^{\circ}}{3} + 2 πn < x < \frac{5 π + 3 \cdot 4 5 ^{\circ}}{3} + 2 πn

Combinar os intervalos

\frac{π + 3 \cdot 4 5 ^{\circ}}{3} + 2 πn < x < \frac{5 π + 3 \cdot 4 5 ^{\circ}}{3} + 2 πn and 0^{\circ} \leq x \leq 36 0^{\circ}

\frac{π + 3 \cdot 4 5 ^{\circ}}{3} < x < \frac{5 π + 3 \cdot 4 5 ^{\circ}}{3}

Gráfico

Exemplos populares

(2sin(x)-1)(-2cos(x)+sqrt(2))<= 0

(2 sin (x) - 1) (- 2 cos (x) + 2) \leq 0

3cos(x)+11/2 >4

3 cos (x) + \frac{11}{2} > 4

cos(x^4)+sin(x^4)<0.5

cos (x^{4}) + sin (x^{4}) < 0.5

cos((x-60)/2)>0

cos (\frac{x - 60}{2}) > 0

sin(2x-(2pi)/3)<= (sqrt(2))/2

sin (2 x - \frac{2 π}{3}) \leq \frac{2}{2}