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Popular >

60sin(45)=400sin(θ)

Solución

60 sin (4 5^{\circ}) = 400 sin (θ)

Solución

θ = 0.10626 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.10626 \dots + 36 0^{\circ} n

+1

radianes

θ = 0.10626 \dots + 2 πn, θ = π - 0.10626 \dots + 2 πn

Pasos de solución

60 sin (4 5^{\circ}) = 400 sin (θ)

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

Utilizar la siguiente identidad trivial:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= \frac{2}{2}

60 \cdot \frac{2}{2} = 400 sin (θ)

Intercambiar lados

400 sin (θ) = 60 \cdot \frac{2}{2}

Multiplicar fracciones:

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

400 sin (θ) = \frac{2 \cdot 60}{2}

Dividir:

\frac{60}{2} = 30

400 sin (θ) = 302

Dividir ambos lados entre

400

400 sin (θ) = 302

Dividir ambos lados entre

400

\frac{400 sin ( θ )}{400} = \frac{30 2}{400}

Simplificar

sin (θ) = \frac{3 2}{40}

sin (θ) = \frac{3 2}{40}

Aplicar propiedades trigonométricas inversas

sin (θ) = \frac{3 2}{40}

Soluciones generales para

sin (θ) = \frac{3 2}{40}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

θ = arcsin (\frac{3 2}{40}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{3 2}{40}) + 36 0^{\circ} n

θ = arcsin (\frac{3 2}{40}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{3 2}{40}) + 36 0^{\circ} n

Mostrar soluciones en forma decimal

θ = 0.10626 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.10626 \dots + 36 0^{\circ} n

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