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Popular >

10=sqrt(65)sqrt(5)cos(θ)

Solución

10 = 65 \cdot 5 \cdot cos (θ)

Solución

θ = 0.98279 \dots + 2 πn, θ = 2 π - 0.98279 \dots + 2 πn

+1

Grados

θ = 56.30993 \dots^{\circ} + 36 0^{\circ} n, θ = 303.69006 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

10 = 655 cos (θ)

Intercambiar lados

655 cos (θ) = 10

Simplificar

655 : 513

655

Factorizar entero

65 = 5 \cdot 13

= 5 \cdot 13 5

Aplicar las leyes de los exponentes:

5 \cdot 13 = 513

= 5135

Aplicar las leyes de los exponentes:

a a = a

55 = 5

= 513

513 cos (θ) = 10

Dividir ambos lados entre

513

513 cos (θ) = 10

Dividir ambos lados entre

513

\frac{5 13 cos ( θ )}{5 13} = \frac{10}{5 13}

Simplificar

\frac{5 13 cos ( θ )}{5 13} = \frac{10}{5 13}

Simplificar

\frac{5 13 cos ( θ )}{5 13} : cos (θ)

\frac{5 13 cos ( θ )}{5 13}

Dividir:

\frac{5}{5} = 1

= \frac{13 cos ( θ )}{13}

Eliminar los terminos comunes:

13

= cos (θ)

Simplificar

\frac{10}{5 13} : \frac{2 13}{13}

\frac{10}{5 13}

Dividir:

\frac{10}{5} = 2

= \frac{2}{13}

Racionalizar

\frac{2}{13} : \frac{2 13}{13}

\frac{2}{13}

Multiplicar por el conjugado

\frac{13}{13}

= \frac{2 13}{13 13}

1313 = 13

1313

Aplicar las leyes de los exponentes:

a a = a

1313 = 13

= 13

= \frac{2 13}{13}

= \frac{2 13}{13}

cos (θ) = \frac{2 13}{13}

cos (θ) = \frac{2 13}{13}

cos (θ) = \frac{2 13}{13}

Aplicar propiedades trigonométricas inversas

cos (θ) = \frac{2 13}{13}

Soluciones generales para

cos (θ) = \frac{2 13}{13}

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

θ = arccos (\frac{2 13}{13}) + 2 πn, θ = 2 π - arccos (\frac{2 13}{13}) + 2 πn

θ = arccos (\frac{2 13}{13}) + 2 πn, θ = 2 π - arccos (\frac{2 13}{13}) + 2 πn

Mostrar soluciones en forma decimal

θ = 0.98279 \dots + 2 πn, θ = 2 π - 0.98279 \dots + 2 πn

Ejemplos populares

1sin(40)=1.5sin(x)

1 sin (4 0^{\circ}) = 1.5 sin (x)

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3sin(2x)-9sin(x)-4cos(x)+6=0

3 sin (2 x) - 9 sin (x) - 4 cos (x) + 6 = 0

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