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sin(α)=(120sin(60))/(1200)

Solución

sin (α) = \frac{120 sin ( 6 0 ^{\circ} )}{1200}

α = 0.08671 \dots + 36 0^{\circ} n, α = 18 0^{\circ} - 0.08671 \dots + 36 0^{\circ} n

radianes

α = 0.08671 \dots + 2 πn, α = π - 0.08671 \dots + 2 πn

Pasos de solución

sin (α) = \frac{120 sin ( 6 0 ^{\circ} )}{1200}

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 0^{\circ})

Utilizar la siguiente identidad trivial:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 0^{\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{3}{2}

= \frac{3}{2}

sin (α) = \frac{120 \cdot \frac{3}{2}}{1200}

Simplificar

\frac{120 \cdot \frac{3}{2}}{1200} : \frac{3}{20}

\frac{120 \cdot \frac{3}{2}}{1200}

Multiplicar

120 \cdot \frac{3}{2} : 603

120 \cdot \frac{3}{2}

Multiplicar fracciones:

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

= \frac{3 \cdot 120}{2}

Dividir:

\frac{120}{2} = 60

= 603

= \frac{60 3}{1200}

Eliminar los terminos comunes:

60

= \frac{3}{20}

Aplicar propiedades trigonométricas inversas

sin (α) = \frac{3}{20}

Soluciones generales para

sin (α) = \frac{3}{20}

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

α = arcsin (\frac{3}{20}) + 36 0^{\circ} n, α = 18 0^{\circ} - arcsin (\frac{3}{20}) + 36 0^{\circ} n

α = arcsin (\frac{3}{20}) + 36 0^{\circ} n, α = 18 0^{\circ} - arcsin (\frac{3}{20}) + 36 0^{\circ} n

Mostrar soluciones en forma decimal

α = 0.08671 \dots + 36 0^{\circ} n, α = 18 0^{\circ} - 0.08671 \dots + 36 0^{\circ} n

15.8 \cdot sin (30 x - 90) + 5 = 17

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cos^{2} (θ) - 1 = sin^{2} (θ)

- 3 cos^{2} (u) sin (u) - 2 sin (2 u) = 0

cot (θ) = - \frac{7}{24}