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Popular >

sin(θ)=(0.000069)2(500*10^{-9})

Solución

sin (θ) = (0.000069) 2 (500 \cdot 1 0^{- 9})

Solución

θ = 0 + 2 πn, θ = π - 0 + 2 πn

+1

radianes

θ = 0 + 2 πn, θ = π + 2 πn

Pasos de solución

sin (θ) = (0.000069) \cdot 2 (500 \cdot 1 0^{- 9})

Simplificar

0.000069 \cdot 2 \cdot 500 \cdot 1 0^{- 9} : \frac{0.000069}{1000000}

0.000069 \cdot 2 \cdot 500 \cdot 1 0^{- 9}

Aplicar las leyes de los exponentes:

a^{- b} = \frac{1}{a ^{b}}

1 0^{- 9} = \frac{1}{1 0 ^{9}}

= 2 \cdot 500 \cdot 0.000069 \cdot \frac{1}{1 0 ^{9}}

Multiplicar fracciones:

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

= 0.000069 \cdot \frac{1 \cdot 2 \cdot 500}{1 0 ^{9}}

\frac{1 \cdot 2 \cdot 500}{1 0 ^{9}} = \frac{1}{1000000}

\frac{1 \cdot 2 \cdot 500}{1 0 ^{9}}

Multiplicar los numeros:

1 \cdot 2 \cdot 500 = 1000

= \frac{1000}{1 0 ^{9}}

Factorizar

1000 : 2^{3} \cdot 5^{3}

Factorizar

1000 = 2^{3} \cdot 5^{3}

Factorizar

1 0^{9} : 2^{9} \cdot 5^{9}

Factorizar

10 = 2 \cdot 5

= (2 \cdot 5)^{9}

Aplicar las leyes de los exponentes:

(ab)^{c} = a^{c} b^{c}

= 2^{9} \cdot 5^{9}

= \frac{2 ^{3} \cdot 5 ^{3}}{2 ^{9} \cdot 5 ^{9}}

Cancelar

\frac{2 ^{3} \cdot 5 ^{3}}{2 ^{9} \cdot 5 ^{9}} : \frac{1}{2 ^{6} \cdot 5 ^{6}}

\frac{2 ^{3} \cdot 5 ^{3}}{2 ^{9} \cdot 5 ^{9}}

Aplicar las leyes de los exponentes:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{2 ^{3}}{2 ^{9}} = \frac{1}{2 ^{9 - 3}}

= \frac{5 ^{3}}{5 ^{9} \cdot 2 ^{9 - 3}}

Restar:

9 - 3 = 6

= \frac{5 ^{3}}{5 ^{9} \cdot 2 ^{6}}

Aplicar las leyes de los exponentes:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{5 ^{3}}{5 ^{9}} = \frac{1}{5 ^{9 - 3}}

= \frac{1}{2 ^{6} \cdot 5 ^{9 - 3}}

Restar:

9 - 3 = 6

= \frac{1}{2 ^{6} \cdot 5 ^{6}}

= \frac{1}{2 ^{6} \cdot 5 ^{6}}

2^{6} \cdot 5^{6} = 1000000

2^{6} \cdot 5^{6}

2^{6} = 64

= 5^{6} \cdot 64

5^{6} = 15625

= 64 \cdot 15625

Multiplicar los numeros:

64 \cdot 15625 = 1000000

= 1000000

= \frac{1}{1000000}

= 0.000069 \cdot \frac{1}{1000000}

Multiplicar fracciones:

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

= \frac{1 \cdot 0.000069}{1000000}

Multiplicar los numeros:

1 \cdot 0.000069 = 0.000069

= \frac{0.000069}{1000000}

Aplicar propiedades trigonométricas inversas

sin (θ) = \frac{0.000069}{1000000}

Soluciones generales para

sin (θ) = \frac{0.000069}{1000000}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

θ = arcsin (\frac{0.000069}{1000000}) + 2 πn, θ = π - arcsin (\frac{0.000069}{1000000}) + 2 πn

θ = arcsin (\frac{0.000069}{1000000}) + 2 πn, θ = π - arcsin (\frac{0.000069}{1000000}) + 2 πn

Mostrar soluciones en forma decimal

θ = 0 + 2 πn, θ = π - 0 + 2 πn

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