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589sin(45)=443sin(x)

Solución

589 \cdot sin (4 5^{\circ}) = 443 \cdot sin (x)

Solución

x = 1.22306 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.22306 \dots + 36 0^{\circ} n

+1

radianes

x = 1.22306 \dots + 2 πn, x = π - 1.22306 \dots + 2 πn

Pasos de solución

589 sin (4 5^{\circ}) = 443 sin (x)

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

Utilizar la siguiente identidad trivial:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= \frac{2}{2}

589 \cdot \frac{2}{2} = 443 sin (x)

Intercambiar lados

443 sin (x) = 589 \cdot \frac{2}{2}

Dividir ambos lados entre

443

443 sin (x) = 589 \cdot \frac{2}{2}

Dividir ambos lados entre

443

\frac{443 sin ( x )}{443} = \frac{589 \cdot \frac{2}{2}}{443}

Simplificar

\frac{443 sin ( x )}{443} = \frac{589 \cdot \frac{2}{2}}{443}

Simplificar

\frac{443 sin ( x )}{443} : sin (x)

\frac{443 sin ( x )}{443}

Dividir:

\frac{443}{443} = 1

= sin (x)

Simplificar

\frac{589 \cdot \frac{2}{2}}{443} : \frac{589 2}{886}

\frac{589 \cdot \frac{2}{2}}{443}

Multiplicar

589 \cdot \frac{2}{2} : \frac{589}{2}

589 \cdot \frac{2}{2}

Multiplicar fracciones:

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

= \frac{2 \cdot 589}{2}

Aplicar las leyes de los exponentes:

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

= \frac{589 \cdot 2 ^{\frac{1}{2}}}{2}

Aplicar las leyes de los exponentes:

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

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

= \frac{589}{2 ^{1 - \frac{1}{2}}}

Restar:

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

= \frac{589}{2 ^{\frac{1}{2}}}

Aplicar las leyes de los exponentes:

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

= \frac{589}{2}

= \frac{\frac{589}{2}}{443}

Aplicar las propiedades de las fracciones:

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

= \frac{589}{2 \cdot 443}

Racionalizar

\frac{589}{443 2} : \frac{589 2}{886}

\frac{589}{443 2}

Multiplicar por el conjugado

\frac{2}{2}

= \frac{589 2}{2 \cdot 443 2}

2 \cdot 4432 = 886

2 \cdot 4432

Aplicar las leyes de los exponentes:

a a = a

22 = 2

= 443 \cdot 2

Multiplicar los numeros:

443 \cdot 2 = 886

= 886

= \frac{589 2}{886}

= \frac{589 2}{886}

sin (x) = \frac{589 2}{886}

sin (x) = \frac{589 2}{886}

sin (x) = \frac{589 2}{886}

Aplicar propiedades trigonométricas inversas

sin (x) = \frac{589 2}{886}

Soluciones generales para

sin (x) = \frac{589 2}{886}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x = arcsin (\frac{589 2}{886}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{589 2}{886}) + 36 0^{\circ} n

x = arcsin (\frac{589 2}{886}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{589 2}{886}) + 36 0^{\circ} n

Mostrar soluciones en forma decimal

x = 1.22306 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.22306 \dots + 36 0^{\circ} n

Ejemplos populares

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\frac{13}{12} = cosh (\frac{x}{120})

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