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Popular >

5=20.39sin(θ)cos(θ)

Solución

5 = 20.39 sin (θ) cos (θ)

Solución

θ = \frac{0.51259 \dots}{2} + πn, θ = \frac{π}{2} - \frac{0.51259 \dots}{2} + πn

Grados

θ = 14.68463 \dots^{\circ} + 18 0^{\circ} n, θ = 75.31536 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

5 = 20.39 sin (θ) cos (θ)

Intercambiar lados

20.39 sin (θ) cos (θ) = 5

Re-escribir usando identidades trigonométricas

20.39 sin (θ) cos (θ)

Utilizar la identidad trigonométrica del ángulo doble:

2 sin (x) cos (x) = sin (2 x)

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

= 20.39 \cdot \frac{sin ( 2 θ )}{2}

20.39 \cdot \frac{sin ( 2 θ )}{2} = 5

Simplificar

20.39 \cdot \frac{sin ( 2 θ )}{2} : \frac{20.39 sin ( 2 θ )}{2}

20.39 \cdot \frac{sin ( 2 θ )}{2}

Multiplicar fracciones:

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

= \frac{sin ( 2 θ ) \cdot 20.39}{2}

\frac{20.39 sin ( 2 θ )}{2} = 5

Multiplicar ambos lados por

2

\frac{20.39 sin ( 2 θ )}{2} = 5

Multiplicar ambos lados por

2

\frac{20.39 sin ( 2 θ )}{2} \cdot 2 = 5 \cdot 2

Simplificar

\frac{20.39 sin ( 2 θ )}{2} \cdot 2 = 5 \cdot 2

Simplificar

\frac{20.39 sin ( 2 θ )}{2} \cdot 2 : 20.39 sin (2 θ)

\frac{20.39 sin ( 2 θ )}{2} \cdot 2

Multiplicar fracciones:

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

= \frac{20.39 sin ( 2 θ ) \cdot 2}{2}

Eliminar los terminos comunes:

2

= 20.39 sin (2 θ)

Simplificar

5 \cdot 2 : 10

5 \cdot 2

Multiplicar los numeros:

5 \cdot 2 = 10

= 10

20.39 sin (2 θ) = 10

20.39 sin (2 θ) = 10

20.39 sin (2 θ) = 10

Dividir ambos lados entre

20.39

20.39 sin (2 θ) = 10

Dividir ambos lados entre

20.39

\frac{20.39 sin ( 2 θ )}{20.39} = \frac{10}{20.39}

Simplificar

sin (2 θ) = 0.49043 \dots

sin (2 θ) = 0.49043 \dots

Aplicar propiedades trigonométricas inversas

sin (2 θ) = 0.49043 \dots

Soluciones generales para

sin (2 θ) = 0.49043 \dots

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

2 θ = arcsin (0.49043 \dots) + 2 πn, 2 θ = π - arcsin (0.49043 \dots) + 2 πn

2 θ = arcsin (0.49043 \dots) + 2 πn, 2 θ = π - arcsin (0.49043 \dots) + 2 πn

Resolver

2 θ = arcsin (0.49043 \dots) + 2 πn : θ = \frac{arcsin ( 0.49043 \dots )}{2} + πn

2 θ = arcsin (0.49043 \dots) + 2 πn

Dividir ambos lados entre

2

2 θ = arcsin (0.49043 \dots) + 2 πn

Dividir ambos lados entre

2

\frac{2 θ}{2} = \frac{arcsin ( 0.49043 \dots )}{2} + \frac{2 πn}{2}

Simplificar

θ = \frac{arcsin ( 0.49043 \dots )}{2} + πn

θ = \frac{arcsin ( 0.49043 \dots )}{2} + πn

Resolver

2 θ = π - arcsin (0.49043 \dots) + 2 πn : θ = \frac{π}{2} - \frac{arcsin ( 0.49043 \dots )}{2} + πn

2 θ = π - arcsin (0.49043 \dots) + 2 πn

Dividir ambos lados entre

2

2 θ = π - arcsin (0.49043 \dots) + 2 πn

Dividir ambos lados entre

2

\frac{2 θ}{2} = \frac{π}{2} - \frac{arcsin ( 0.49043 \dots )}{2} + \frac{2 πn}{2}

Simplificar

θ = \frac{π}{2} - \frac{arcsin ( 0.49043 \dots )}{2} + πn

θ = \frac{π}{2} - \frac{arcsin ( 0.49043 \dots )}{2} + πn

θ = \frac{arcsin ( 0.49043 \dots )}{2} + πn, θ = \frac{π}{2} - \frac{arcsin ( 0.49043 \dots )}{2} + πn

Mostrar soluciones en forma decimal

θ = \frac{0.51259 \dots}{2} + πn, θ = \frac{π}{2} - \frac{0.51259 \dots}{2} + πn

Ejemplos populares

cos(4x)=cos(3x)

cos (4 x) = cos (3 x)

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12 sin^{2} (θ) = 9

2cos(x)+sqrt(3)=0,0<= x<= 2pi

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