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Popular Trigonometria >

(sin(60))/(174.36)=(sin(x))/(200)

Solução

\frac{sin ( 6 0 ^{\circ} )}{174.36} = \frac{sin ( x )}{200}

Solução

x = 1.45563 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.45563 \dots + 36 0^{\circ} n

Radianos

x = 1.45563 \dots + 2 πn, x = π - 1.45563 \dots + 2 πn

Passos da solução

\frac{sin ( 6 0 ^{\circ} )}{174.36} = \frac{sin ( x )}{200}

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

sin (6 0^{\circ})

Utilizar a seguinte identidade trivial:

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

sin (6 0^{\circ})

sin (x)

tabela de periodicidade com ciclo de

36 0^{\circ} n

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}

\frac{\frac{3}{2}}{174.36} = \frac{sin ( x )}{200}

Trocar lados

\frac{sin ( x )}{200} = \frac{\frac{3}{2}}{174.36}

Multiplicar ambos os lados por

100

\frac{sin ( x )}{200} = \frac{\frac{3}{2}}{174.36}

Multiplicar ambos os lados por

100

\frac{sin ( x )}{200} \cdot 100 = \frac{\frac{3}{2}}{174.36} \cdot 100

Simplificar

\frac{sin ( x )}{200} \cdot 100 = \frac{\frac{3}{2}}{174.36} \cdot 100

Simplificar

\frac{sin ( x )}{200} \cdot 100 : \frac{sin ( x )}{2}

\frac{sin ( x )}{200} \cdot 100

Multiplicar frações:

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

= \frac{sin ( x ) \cdot 100}{200}

Eliminar o fator comum:

100

= \frac{sin ( x )}{2}

Simplificar

\frac{\frac{3}{2}}{174.36} \cdot 100 : \frac{100 3}{348.72}

\frac{\frac{3}{2}}{174.36} \cdot 100

\frac{\frac{3}{2}}{174.36} = \frac{3}{348.72}

\frac{\frac{3}{2}}{174.36}

Aplicar as propriedades das frações:

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

= \frac{3}{2 \cdot 174.36}

Multiplicar os números:

2 \cdot 174.36 = 348.72

= \frac{3}{348.72}

= 100 \cdot \frac{3}{348.72}

Multiplicar frações:

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

= \frac{3 \cdot 100}{348.72}

\frac{sin ( x )}{2} = \frac{100 3}{348.72}

\frac{sin ( x )}{2} = \frac{100 3}{348.72}

\frac{sin ( x )}{2} = \frac{100 3}{348.72}

Multiplicar ambos os lados por

2

\frac{sin ( x )}{2} = \frac{100 3}{348.72}

Multiplicar ambos os lados por

2

\frac{2 sin ( x )}{2} = \frac{2 \cdot 100 3}{348.72}

Simplificar

\frac{2 sin ( x )}{2} = \frac{2 \cdot 100 3}{348.72}

Simplificar

\frac{2 sin ( x )}{2} : sin (x)

\frac{2 sin ( x )}{2}

Dividir:

\frac{2}{2} = 1

= sin (x)

Simplificar

\frac{2 \cdot 100 3}{348.72} : 0.99337 \dots

\frac{2 \cdot 100 3}{348.72}

Multiplicar os números:

2 \cdot 100 = 200

= \frac{200 3}{348.72}

Converter o elemento em uma forma decimal

3 = 1.73205 \dots

= \frac{200 \cdot 1.73205 \dots}{348.72}

Multiplicar os números:

200 \cdot 1.73205 \dots = 346.41016 \dots

= \frac{346.41016 \dots}{348.72}

Dividir:

\frac{346.41016 \dots}{348.72} = 0.99337 \dots

= 0.99337 \dots

sin (x) = 0.99337 \dots

sin (x) = 0.99337 \dots

sin (x) = 0.99337 \dots

Aplique as propriedades trigonométricas inversas

sin (x) = 0.99337 \dots

Soluções gerais para

sin (x) = 0.99337 \dots

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

x = arcsin (0.99337 \dots) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.99337 \dots) + 36 0^{\circ} n

x = arcsin (0.99337 \dots) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.99337 \dots) + 36 0^{\circ} n

Mostrar soluções na forma decimal

x = 1.45563 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.45563 \dots + 36 0^{\circ} n

Gráfico

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