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Popular >

(706.32)/(sin(45)1.5+cos(45)0.5)

Solución

\frac{706.32}{sin ( 4 5 ^{\circ} ) 1.5 + cos ( 4 5 ^{\circ} ) 0.5}

Solución

\frac{8829 2}{25}

Notación decimal

499.44366 \dots

Pasos de solución

\frac{706.32}{sin ( 4 5 ^{\circ} ) \cdot 1.5 + cos ( 4 5 ^{\circ} ) \cdot 0.5}

= \frac{\frac{17658}{25}}{sin ( 4 5 ^{\circ} ) \frac{3}{2} + cos ( 4 5 ^{\circ} ) \frac{1}{2}}

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}

Utilizar la siguiente identidad trivial:

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

cos (4 5^{\circ})

cos (x)

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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

= \frac{\frac{17658}{25}}{\frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2}}

Simplificar

\frac{\frac{17658}{25}}{\frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2}} : \frac{8829 2}{25}

\frac{\frac{17658}{25}}{\frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2}}

Aplicar las propiedades de las fracciones:

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

= \frac{17658}{25 ( \frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2} )}

\frac{2}{2} \cdot \frac{3}{2} = \frac{3 2}{4}

\frac{2}{2} \cdot \frac{3}{2}

Multiplicar fracciones:

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

= \frac{2 \cdot 3}{2 \cdot 2}

Multiplicar los numeros:

2 \cdot 2 = 4

= \frac{3 2}{4}

\frac{2}{2} \cdot \frac{1}{2} = \frac{2}{4}

\frac{2}{2} \cdot \frac{1}{2}

Multiplicar fracciones:

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

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

Multiplicar:

2 \cdot 1 = 2

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

Multiplicar los numeros:

2 \cdot 2 = 4

= \frac{2}{4}

= \frac{17658}{25 ( \frac{2}{4} + \frac{3 2}{4} )}

Combinar las fracciones usando el mínimo común denominador:

2

Aplicar la regla

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

= \frac{3 2 + 2}{4}

Sumar elementos similares:

32 + 2 = 42

= \frac{4 2}{4}

Dividir:

\frac{4}{4} = 1

= 2

= \frac{17658}{25 ( 2 )}

Quitar los parentesis:

(a) = a

= \frac{17658}{25 2}

Factorizar

17658 : 3^{4} \cdot 2 \cdot 109

Factorizar

17658 = 3^{4} \cdot 2 \cdot 109

= \frac{3 ^{4} \cdot 2 \cdot 109}{25 2}

Cancelar

\frac{2 \cdot 3 ^{4} \cdot 109}{25 2} : \frac{2 \cdot 3 ^{4} \cdot 109}{25}

\frac{2 \cdot 3 ^{4} \cdot 109}{25 2}

Aplicar las leyes de los exponentes:

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

= \frac{3 ^{4} \cdot 2 \cdot 109}{25 \cdot 2 ^{\frac{1}{2}}}

Aplicar las leyes de los exponentes:

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

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

= \frac{3 ^{4} \cdot 109 \cdot 2 ^{- \frac{1}{2} + 1}}{25}

Restar:

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

= \frac{3 ^{4} \cdot 109 \cdot 2 ^{\frac{1}{2}}}{25}

Aplicar las leyes de los exponentes:

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

= \frac{3 ^{4} \cdot 109 2}{25}

= \frac{2 \cdot 3 ^{4} \cdot 109}{25}

2 \cdot 3^{4} \cdot 109 = 88292

2 \cdot 3^{4} \cdot 109

3^{4} = 81

= 81 \cdot 1092

Multiplicar los numeros:

81 \cdot 109 = 8829

= 88292

= \frac{8829 2}{25}

= \frac{8829 2}{25}

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