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Popular Trigonometría >

2sqrt(3)sin(2θ)=sqrt(3),0<= θ<2pi

Solución

23 sin (2 θ) = 3, 0 \leq θ < 2 π

Solución

θ = \frac{π}{12}, θ = \frac{5 π}{12}, θ = \frac{13 π}{12}, θ = \frac{17 π}{12}

+1

Grados

θ = 1 5^{\circ}, θ = 7 5^{\circ}, θ = 19 5^{\circ}, θ = 25 5^{\circ}

Pasos de solución

23 sin (2 θ) = 3, 0 \leq θ < 2 π

Dividir ambos lados entre

23

23 sin (2 θ) = 3

Dividir ambos lados entre

23

\frac{2 3 sin ( 2 θ )}{2 3} = \frac{3}{2 3}

Simplificar

sin (2 θ) = \frac{1}{2}

sin (2 θ) = \frac{1}{2}

Soluciones generales para

sin (2 θ) = \frac{1}{2}

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}

2 θ = \frac{π}{6} + 2 πn, 2 θ = \frac{5 π}{6} + 2 πn

2 θ = \frac{π}{6} + 2 πn, 2 θ = \frac{5 π}{6} + 2 πn

Resolver

2 θ = \frac{π}{6} + 2 πn : θ = \frac{π}{12} + πn

2 θ = \frac{π}{6} + 2 πn

Dividir ambos lados entre

2

2 θ = \frac{π}{6} + 2 πn

Dividir ambos lados entre

2

\frac{2 θ}{2} = \frac{\frac{π}{6}}{2} + \frac{2 πn}{2}

Simplificar

\frac{2 θ}{2} = \frac{\frac{π}{6}}{2} + \frac{2 πn}{2}

Simplificar

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

Dividir:

\frac{2}{2} = 1

= θ

Simplificar

\frac{\frac{π}{6}}{2} + \frac{2 πn}{2} : \frac{π}{12} + πn

\frac{\frac{π}{6}}{2} + \frac{2 πn}{2}

\frac{\frac{π}{6}}{2} = \frac{π}{12}

\frac{\frac{π}{6}}{2}

Aplicar las propiedades de las fracciones:

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

= \frac{π}{6 \cdot 2}

Multiplicar los numeros:

6 \cdot 2 = 12

= \frac{π}{12}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Dividir:

\frac{2}{2} = 1

= πn

= \frac{π}{12} + πn

θ = \frac{π}{12} + πn

θ = \frac{π}{12} + πn

θ = \frac{π}{12} + πn

Resolver

2 θ = \frac{5 π}{6} + 2 πn : θ = \frac{5 π}{12} + πn

2 θ = \frac{5 π}{6} + 2 πn

Dividir ambos lados entre

2

2 θ = \frac{5 π}{6} + 2 πn

Dividir ambos lados entre

2

\frac{2 θ}{2} = \frac{\frac{5 π}{6}}{2} + \frac{2 πn}{2}

Simplificar

\frac{2 θ}{2} = \frac{\frac{5 π}{6}}{2} + \frac{2 πn}{2}

Simplificar

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

Dividir:

\frac{2}{2} = 1

= θ

Simplificar

\frac{\frac{5 π}{6}}{2} + \frac{2 πn}{2} : \frac{5 π}{12} + πn

\frac{\frac{5 π}{6}}{2} + \frac{2 πn}{2}

\frac{\frac{5 π}{6}}{2} = \frac{5 π}{12}

\frac{\frac{5 π}{6}}{2}

Aplicar las propiedades de las fracciones:

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

= \frac{5 π}{6 \cdot 2}

Multiplicar los numeros:

6 \cdot 2 = 12

= \frac{5 π}{12}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Dividir:

\frac{2}{2} = 1

= πn

= \frac{5 π}{12} + πn

θ = \frac{5 π}{12} + πn

θ = \frac{5 π}{12} + πn

θ = \frac{5 π}{12} + πn

θ = \frac{π}{12} + πn, θ = \frac{5 π}{12} + πn

Soluciones para el rango

0 \leq θ < 2 π

θ = \frac{π}{12}, θ = \frac{5 π}{12}, θ = \frac{13 π}{12}, θ = \frac{17 π}{12}

Gráfica

Ejemplos populares

cos(x)-sqrt(3)=3cos(x)

2tan^2(x)-7sec(x)+5=0

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