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55^2=50^2+90^2-25090*cos(x)

Solución

5 5^{2} = 5 0^{2} + 9 0^{2} - 2 \cdot 50 \cdot 90 \cdot cos (x)

Solución

x = 0.57043 \dots + 2 πn, x = 2 π - 0.57043 \dots + 2 πn

+1

Grados

x = 32.68346 \dots^{\circ} + 36 0^{\circ} n, x = 327.31653 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

5 5^{2} = 5 0^{2} + 9 0^{2} - 2 \cdot 50 \cdot 90 cos (x)

Intercambiar lados

5 0^{2} + 9 0^{2} - 2 \cdot 50 \cdot 90 cos (x) = 5 5^{2}

Multiplicar los numeros:

2 \cdot 50 \cdot 90 = 9000

5 0^{2} + 9 0^{2} - 9000 cos (x) = 5 5^{2}

5 0^{2} = 2500

2500 + 9 0^{2} - 9000 cos (x) = 5 5^{2}

9 0^{2} = 8100

2500 + 8100 - 9000 cos (x) = 5 5^{2}

Sumar:

2500 + 8100 = 10600

- 9000 cos (x) + 10600 = 5 5^{2}

5 5^{2} = 3025

- 9000 cos (x) + 10600 = 3025

Mover

10600

al lado derecho

- 9000 cos (x) + 10600 = 3025

Restar

10600

de ambos lados

- 9000 cos (x) + 10600 - 10600 = 3025 - 10600

Simplificar

- 9000 cos (x) = - 7575

- 9000 cos (x) = - 7575

Dividir ambos lados entre

- 9000

- 9000 cos (x) = - 7575

Dividir ambos lados entre

- 9000

\frac{- 9000 cos ( x )}{- 9000} = \frac{- 7575}{- 9000}

Simplificar

\frac{- 9000 cos ( x )}{- 9000} = \frac{- 7575}{- 9000}

Simplificar

\frac{- 9000 cos ( x )}{- 9000} : cos (x)

\frac{- 9000 cos ( x )}{- 9000}

Aplicar las propiedades de las fracciones:

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

= \frac{9000 cos ( x )}{9000}

Dividir:

\frac{9000}{9000} = 1

= cos (x)

Simplificar

\frac{- 7575}{- 9000} : \frac{101}{120}

\frac{- 7575}{- 9000}

Aplicar las propiedades de las fracciones:

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

= \frac{7575}{9000}

Eliminar los terminos comunes:

75

= \frac{101}{120}

cos (x) = \frac{101}{120}

cos (x) = \frac{101}{120}

cos (x) = \frac{101}{120}

Aplicar propiedades trigonométricas inversas

cos (x) = \frac{101}{120}

Soluciones generales para

cos (x) = \frac{101}{120}

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

x = arccos (\frac{101}{120}) + 2 πn, x = 2 π - arccos (\frac{101}{120}) + 2 πn

x = arccos (\frac{101}{120}) + 2 πn, x = 2 π - arccos (\frac{101}{120}) + 2 πn

Mostrar soluciones en forma decimal

x = 0.57043 \dots + 2 πn, x = 2 π - 0.57043 \dots + 2 πn

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