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Popular >

12^2=10^2+12^2-2(10)(12)cos(b)

Solución

1 2^{2} = 1 0^{2} + 1 2^{2} - 2 (10) (12) cos (b)

Solución

b = 1.14102 \dots + 2 πn, b = 2 π - 1.14102 \dots + 2 πn

+1

Grados

b = 65.37568 \dots^{\circ} + 36 0^{\circ} n, b = 294.62431 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

1 2^{2} = 1 0^{2} + 1 2^{2} - 2 (10) (12) cos (b)

Intercambiar lados

1 0^{2} + 1 2^{2} - 2 \cdot 10 \cdot 12 cos (b) = 1 2^{2}

Restar

1 2^{2}

de ambos lados

1 0^{2} + 1 2^{2} - 2 \cdot 10 \cdot 12 cos (b) - 1 2^{2} = 1 2^{2} - 1 2^{2}

Simplificar

1 0^{2} - 2 \cdot 10 \cdot 12 cos (b) = 0

Multiplicar los numeros:

2 \cdot 10 \cdot 12 = 240

1 0^{2} - 240 cos (b) = 0

1 0^{2} = 100

100 - 240 cos (b) = 0

Mover

100

al lado derecho

100 - 240 cos (b) = 0

Restar

100

de ambos lados

100 - 240 cos (b) - 100 = 0 - 100

Simplificar

- 240 cos (b) = - 100

- 240 cos (b) = - 100

Dividir ambos lados entre

- 240

- 240 cos (b) = - 100

Dividir ambos lados entre

- 240

\frac{- 240 cos ( b )}{- 240} = \frac{- 100}{- 240}

Simplificar

\frac{- 240 cos ( b )}{- 240} = \frac{- 100}{- 240}

Simplificar

\frac{- 240 cos ( b )}{- 240} : cos (b)

\frac{- 240 cos ( b )}{- 240}

Aplicar las propiedades de las fracciones:

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

= \frac{240 cos ( b )}{240}

Dividir:

\frac{240}{240} = 1

= cos (b)

Simplificar

\frac{- 100}{- 240} : \frac{5}{12}

\frac{- 100}{- 240}

Aplicar las propiedades de las fracciones:

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

= \frac{100}{240}

Eliminar los terminos comunes:

20

= \frac{5}{12}

cos (b) = \frac{5}{12}

cos (b) = \frac{5}{12}

cos (b) = \frac{5}{12}

Aplicar propiedades trigonométricas inversas

cos (b) = \frac{5}{12}

Soluciones generales para

cos (b) = \frac{5}{12}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

b = arccos (\frac{5}{12}) + 2 πn, b = 2 π - arccos (\frac{5}{12}) + 2 πn

b = arccos (\frac{5}{12}) + 2 πn, b = 2 π - arccos (\frac{5}{12}) + 2 πn

Mostrar soluciones en forma decimal

b = 1.14102 \dots + 2 πn, b = 2 π - 1.14102 \dots + 2 πn

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