English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(sin(x))/(700)=(sin(45))/(497)

Solución

\frac{sin ( x )}{700} = \frac{sin ( 4 5 ^{\circ} )}{497}

Solución

x = 1.48048 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.48048 \dots + 36 0^{\circ} n

radianes

x = 1.48048 \dots + 2 πn, x = π - 1.48048 \dots + 2 πn

Pasos de solución

\frac{sin ( x )}{700} = \frac{sin ( 4 5 ^{\circ} )}{497}

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}

\frac{sin ( x )}{700} = \frac{\frac{2}{2}}{497}

Multiplicar ambos lados por

100

\frac{sin ( x )}{700} = \frac{\frac{2}{2}}{497}

Multiplicar ambos lados por

100

\frac{sin ( x )}{700} \cdot 100 = \frac{\frac{2}{2}}{497} \cdot 100

Simplificar

\frac{sin ( x )}{700} \cdot 100 = \frac{\frac{2}{2}}{497} \cdot 100

Simplificar

\frac{sin ( x )}{700} \cdot 100 : \frac{sin ( x )}{7}

\frac{sin ( x )}{700} \cdot 100

Multiplicar fracciones:

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

= \frac{sin ( x ) \cdot 100}{700}

Eliminar los terminos comunes:

100

= \frac{sin ( x )}{7}

Simplificar

\frac{\frac{2}{2}}{497} \cdot 100 : \frac{50 2}{497}

\frac{\frac{2}{2}}{497} \cdot 100

\frac{\frac{2}{2}}{497} = \frac{2}{994}

\frac{\frac{2}{2}}{497}

Aplicar las propiedades de las fracciones:

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

= \frac{2}{2 \cdot 497}

Multiplicar los numeros:

2 \cdot 497 = 994

= \frac{2}{994}

= 100 \cdot \frac{2}{994}

Multiplicar fracciones:

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

= \frac{2 \cdot 100}{994}

Eliminar los terminos comunes:

2

= \frac{50 2}{497}

\frac{sin ( x )}{7} = \frac{50 2}{497}

\frac{sin ( x )}{7} = \frac{50 2}{497}

\frac{sin ( x )}{7} = \frac{50 2}{497}

Multiplicar ambos lados por

7

\frac{sin ( x )}{7} = \frac{50 2}{497}

Multiplicar ambos lados por

7

\frac{7 sin ( x )}{7} = \frac{7 \cdot 50 2}{497}

Simplificar

\frac{7 sin ( x )}{7} = \frac{7 \cdot 50 2}{497}

Simplificar

\frac{7 sin ( x )}{7} : sin (x)

\frac{7 sin ( x )}{7}

Dividir:

\frac{7}{7} = 1

= sin (x)

Simplificar

\frac{7 \cdot 50 2}{497} : \frac{50 2}{71}

\frac{7 \cdot 50 2}{497}

Multiplicar los numeros:

7 \cdot 50 = 350

= \frac{350 2}{497}

Eliminar los terminos comunes:

7

= \frac{50 2}{71}

sin (x) = \frac{50 2}{71}

sin (x) = \frac{50 2}{71}

sin (x) = \frac{50 2}{71}

Aplicar propiedades trigonométricas inversas

sin (x) = \frac{50 2}{71}

Soluciones generales para

sin (x) = \frac{50 2}{71}

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

x = arcsin (\frac{50 2}{71}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{50 2}{71}) + 36 0^{\circ} n

x = arcsin (\frac{50 2}{71}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{50 2}{71}) + 36 0^{\circ} n

Mostrar soluciones en forma decimal

x = 1.48048 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.48048 \dots + 36 0^{\circ} n

Ejemplos populares

25sin(x)-1.5cos(x)=20

25 sin (x) - 1.5 cos (x) = 20

cos(θ)= 1/2 ,0<= θ<= 4pi

cos (θ) = \frac{1}{2}, 0 \leq θ \leq 4 π

sinh^2(x)=2sinh(x)cosh(x)

sinh^{2} (x) = 2 sinh (x) cosh (x)

(cos(x)-1)(sin(x)-1)=0

(cos (x) - 1) (sin (x) - 1) = 0

sec(θ)=(3sqrt(2))/4

sec (θ) = \frac{3 2}{4}