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Popular Trigonometría >

sin((2pi(t+101.75))/(365))=-1

Solución

sin (\frac{2 π ( t + 101.75 )}{365}) = - 1

Solución

t = 364.99999 \dots n + 172

Grados

t = 9854.87407 \dots^{\circ} + 20912.95952 \dots^{\circ} n

Pasos de solución

sin (\frac{2 π ( t + 101.75 )}{365}) = - 1

Soluciones generales para

sin (\frac{2 π ( t + 101.75 )}{365}) = - 1

tabla de valores periódicos con

2 πn

intervalos:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{2 π ( t + 101.75 )}{365} = \frac{3 π}{2} + 2 πn

\frac{2 π ( t + 101.75 )}{365} = \frac{3 π}{2} + 2 πn

Resolver

\frac{2 π ( t + 101.75 )}{365} = \frac{3 π}{2} + 2 πn : t = 364.99999 \dots n + 172

\frac{2 π ( t + 101.75 )}{365} = \frac{3 π}{2} + 2 πn

Multiplicar ambos lados por

365

\frac{2 π ( t + 101.75 )}{365} = \frac{3 π}{2} + 2 πn

Multiplicar ambos lados por

365

\frac{365 \cdot 2 π ( t + 101.75 )}{365} = 365 \cdot \frac{3 π}{2} + 365 \cdot 2 πn

Simplificar

\frac{365 \cdot 2 π ( t + 101.75 )}{365} = 365 \cdot \frac{3 π}{2} + 365 \cdot 2 πn

Simplificar

\frac{365 \cdot 2 π ( t + 101.75 )}{365} : 6.28318 \dots (t + 101.75)

\frac{365 \cdot 2 π ( t + 101.75 )}{365}

Multiplicar los numeros:

365 \cdot 2 = 730

= \frac{730 π ( t + 101.75 )}{365}

Dividir:

\frac{730}{365} = 2

= 2 π (t + 101.75)

Multiplicar los numeros:

2 \cdot 3.14159 \dots = 6.28318 \dots

= 6.28318 \dots (t + 101.75)

Simplificar

365 \cdot \frac{3 π}{2} + 365 \cdot 2 πn : \frac{1095 π}{2} + 730 πn

365 \cdot \frac{3 π}{2} + 365 \cdot 2 πn

365 \cdot \frac{3 π}{2} = \frac{1095 π}{2}

365 \cdot \frac{3 π}{2}

Multiplicar fracciones:

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

= \frac{3 π 365}{2}

Multiplicar los numeros:

3 \cdot 365 = 1095

= \frac{1095 π}{2}

365 \cdot 2 πn = 730 πn

365 \cdot 2 πn

Multiplicar los numeros:

365 \cdot 2 = 730

= 730 πn

= \frac{1095 π}{2} + 730 πn

6.28318 \dots (t + 101.75) = \frac{1095 π}{2} + 730 πn

6.28318 \dots (t + 101.75) = \frac{1095 π}{2} + 730 πn

6.28318 \dots (t + 101.75) = \frac{1095 π}{2} + 730 πn

Dividir ambos lados entre

6.28318 \dots

6.28318 \dots (t + 101.75) = \frac{1095 π}{2} + 730 πn

Dividir ambos lados entre

6.28318 \dots

\frac{6.28318 \dots ( t + 101.75 )}{6.28318 \dots} = \frac{\frac{1095 π}{2}}{6.28318 \dots} + \frac{730 πn}{6.28318 \dots}

Simplificar

\frac{6.28318 \dots ( t + 101.75 )}{6.28318 \dots} = \frac{\frac{1095 π}{2}}{6.28318 \dots} + \frac{730 πn}{6.28318 \dots}

Simplificar

\frac{6.28318 \dots ( t + 101.75 )}{6.28318 \dots} : t + 101.75

\frac{6.28318 \dots ( t + 101.75 )}{6.28318 \dots}

Eliminar los terminos comunes:

6.28318 \dots

= t + 101.75

Simplificar

\frac{\frac{1095 π}{2}}{6.28318 \dots} + \frac{730 πn}{6.28318 \dots} : 273.75 + 364.99999 \dots n

\frac{\frac{1095 π}{2}}{6.28318 \dots} + \frac{730 πn}{6.28318 \dots}

\frac{\frac{1095 π}{2}}{6.28318 \dots} = \frac{1095 π}{12.56637 \dots}

\frac{\frac{1095 π}{2}}{6.28318 \dots}

Aplicar las propiedades de las fracciones:

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

= \frac{1095 π}{2 \cdot 6.28318 \dots}

Multiplicar los numeros:

2 \cdot 6.28318 \dots = 12.56637 \dots

= \frac{1095 π}{12.56637 \dots}

= \frac{1095 π}{12.56637 \dots} + \frac{730 πn}{6.28318 \dots}

\frac{1095 π}{12.56637 \dots} = 273.75

\frac{1095 π}{12.56637 \dots}

Multiplicar los numeros:

1095 \cdot 3.14159 \dots = 3440.04395 \dots

= \frac{3440.04395 \dots}{12.56637 \dots}

Dividir:

\frac{3440.04395 \dots}{12.56637 \dots} = 273.75

= 273.75

\frac{730 πn}{6.28318 \dots} = 364.99999 \dots n

\frac{730 πn}{6.28318 \dots}

Multiplicar los numeros:

730 \cdot 3.14159 \dots = 2293.36263 \dots

= \frac{2293.36263 \dots n}{6.28318 \dots}

Dividir:

\frac{2293.36263 \dots}{6.28318 \dots} = 364.99999 \dots

= 364.99999 \dots n

= 273.75 + 364.99999 \dots n

t + 101.75 = 273.75 + 364.99999 \dots n

t + 101.75 = 273.75 + 364.99999 \dots n

t + 101.75 = 273.75 + 364.99999 \dots n

Desplace

101.75

a la derecha

t + 101.75 = 273.75 + 364.99999 \dots n

Restar

101.75

de ambos lados

t + 101.75 - 101.75 = 273.75 + 364.99999 \dots n - 101.75

Simplificar

t = 364.99999 \dots n + 172

t = 364.99999 \dots n + 172

t = 364.99999 \dots n + 172

Gráfica

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