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Popular Trigonometría >

90^2=60^2+70^2-2(60)(70)(cos(x))

Solución

9 0^{2} = 6 0^{2} + 7 0^{2} - 2 (60) (70) (cos (x))

Solución

x = 1.52315 \dots + 2 πn, x = 2 π - 1.52315 \dots + 2 πn

+1

Grados

x = 87.27059 \dots^{\circ} + 36 0^{\circ} n, x = 272.72940 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

9 0^{2} = 6 0^{2} + 7 0^{2} - 2 (60) (70) (cos (x))

Intercambiar lados

6 0^{2} + 7 0^{2} - 2 \cdot 60 \cdot 70 cos (x) = 9 0^{2}

Multiplicar los numeros:

2 \cdot 60 \cdot 70 = 8400

6 0^{2} + 7 0^{2} - 8400 cos (x) = 9 0^{2}

6 0^{2} = 3600

3600 + 7 0^{2} - 8400 cos (x) = 9 0^{2}

7 0^{2} = 4900

3600 + 4900 - 8400 cos (x) = 9 0^{2}

Sumar:

3600 + 4900 = 8500

- 8400 cos (x) + 8500 = 9 0^{2}

9 0^{2} = 8100

- 8400 cos (x) + 8500 = 8100

Desplace

8500

a la derecha

- 8400 cos (x) + 8500 = 8100

Restar

8500

de ambos lados

- 8400 cos (x) + 8500 - 8500 = 8100 - 8500

Simplificar

- 8400 cos (x) = - 400

- 8400 cos (x) = - 400

Dividir ambos lados entre

- 8400

- 8400 cos (x) = - 400

Dividir ambos lados entre

- 8400

\frac{- 8400 cos ( x )}{- 8400} = \frac{- 400}{- 8400}

Simplificar

\frac{- 8400 cos ( x )}{- 8400} = \frac{- 400}{- 8400}

Simplificar

\frac{- 8400 cos ( x )}{- 8400} : cos (x)

\frac{- 8400 cos ( x )}{- 8400}

Aplicar las propiedades de las fracciones:

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

= \frac{8400 cos ( x )}{8400}

Dividir:

\frac{8400}{8400} = 1

= cos (x)

Simplificar

\frac{- 400}{- 8400} : \frac{1}{21}

\frac{- 400}{- 8400}

Aplicar las propiedades de las fracciones:

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

= \frac{400}{8400}

Eliminar los terminos comunes:

400

= \frac{1}{21}

cos (x) = \frac{1}{21}

cos (x) = \frac{1}{21}

cos (x) = \frac{1}{21}

Aplicar propiedades trigonométricas inversas

cos (x) = \frac{1}{21}

Soluciones generales para

cos (x) = \frac{1}{21}

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

x = arccos (\frac{1}{21}) + 2 πn, x = 2 π - arccos (\frac{1}{21}) + 2 πn

x = arccos (\frac{1}{21}) + 2 πn, x = 2 π - arccos (\frac{1}{21}) + 2 πn

Mostrar soluciones en forma decimal

x = 1.52315 \dots + 2 πn, x = 2 π - 1.52315 \dots + 2 πn

Gráfica

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