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Popular >

(20.76+51)5.348cos(75)

Solución

(20.76 + 51) 5.348 cos (7 5^{\circ})

Solución

\frac{1199289 ( 6 - 2 )}{12500}

Notación decimal

99.32762 \dots

Pasos de solución

(20.76 + 51) \cdot 5.348 cos (7 5^{\circ})

= (\frac{519}{25} + 51) \frac{1337}{250} cos (7 5^{\circ})

Re-escribir usando identidades trigonométricas:

cos (7 5^{\circ}) = \frac{6 - 2}{4}

cos (7 5^{\circ})

Re-escribir usando identidades trigonométricas:

cos (4 5^{\circ}) cos (3 0^{\circ}) - sin (4 5^{\circ}) sin (3 0^{\circ})

cos (7 5^{\circ})

Escribir

cos (7 5^{\circ})

como

cos (4 5^{\circ} + 3 0^{\circ})

= cos (4 5^{\circ} + 3 0^{\circ})

Utilizar la identidad de suma de ángulos:

cos (s + t) = cos (s) cos (t) - sin (s) sin (t)

= cos (4 5^{\circ}) cos (3 0^{\circ}) - sin (4 5^{\circ}) sin (3 0^{\circ})

= cos (4 5^{\circ}) cos (3 0^{\circ}) - sin (4 5^{\circ}) sin (3 0^{\circ})

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}

Utilizar la siguiente identidad trivial:

cos (3 0^{\circ}) = \frac{3}{2}

cos (3 0^{\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{3}{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:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\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{1}{2}

= \frac{2}{2} \cdot \frac{3}{2} - \frac{2}{2} \cdot \frac{1}{2}

Simplificar

\frac{2}{2} \cdot \frac{3}{2} - \frac{2}{2} \cdot \frac{1}{2} : \frac{6 - 2}{4}

\frac{2}{2} \cdot \frac{3}{2} - \frac{2}{2} \cdot \frac{1}{2}

\frac{2}{2} \cdot \frac{3}{2} = \frac{6}{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 3}{2 \cdot 2}

Multiplicar los numeros:

2 \cdot 2 = 4

= \frac{2 3}{4}

Simplificar

23 : 6

23

Aplicar las leyes de los exponentes:

a b = a \cdot b

23 = 2 \cdot 3

= 2 \cdot 3

Multiplicar los numeros:

2 \cdot 3 = 6

= 6

= \frac{6}{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{6}{4} - \frac{2}{4}

Aplicar la regla

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

= \frac{6 - 2}{4}

= \frac{6 - 2}{4}

= (\frac{519}{25} + 51) \frac{1337}{250} \cdot \frac{6 - 2}{4}

Simplificar

(\frac{519}{25} + 51) \frac{1337}{250} \cdot \frac{6 - 2}{4} : \frac{1199289 ( 6 - 2 )}{12500}

(\frac{519}{25} + 51) \frac{1337}{250} \cdot \frac{6 - 2}{4}

Simplificar

\frac{519}{25} + 51

en una fracción:

\frac{1794}{25}

\frac{519}{25} + 51

Convertir a fracción:

51 = \frac{51 \cdot 25}{25}

= \frac{51 \cdot 25}{25} + \frac{519}{25}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{51 \cdot 25 + 519}{25}

51 \cdot 25 + 519 = 1794

51 \cdot 25 + 519

Multiplicar los numeros:

51 \cdot 25 = 1275

= 1275 + 519

Sumar:

1275 + 519 = 1794

= 1794

= \frac{1794}{25}

= \frac{1794}{25} \cdot \frac{1337}{250} \cdot \frac{6 - 2}{4}

Multiplicar fracciones:

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

= \frac{1794 \cdot 1337 ( 6 - 2 )}{25 \cdot 250 \cdot 4}

Multiplicar los numeros:

1794 \cdot 1337 = 2398578

= \frac{2398578 ( 6 - 2 )}{25 \cdot 250 \cdot 4}

Multiplicar los numeros:

25 \cdot 250 \cdot 4 = 25000

= \frac{2398578 ( 6 - 2 )}{25000}

Eliminar los terminos comunes:

2

= \frac{1199289 ( 6 - 2 )}{12500}

= \frac{1199289 ( 6 - 2 )}{12500}

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