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Popular >

12.3=2.3sin(24x)+14.1

Solución

12.3 = 2.3 sin (24 x) + 14.1

Solución

x = - \frac{0.89884 \dots}{24} + \frac{πn}{12}, x = \frac{π}{24} + \frac{0.89884 \dots}{24} + \frac{πn}{12}

Grados

x = - 2.14583 \dots^{\circ} + 1 5^{\circ} n, x = 9.64583 \dots^{\circ} + 1 5^{\circ} n

Pasos de solución

12.3 = 2.3 sin (24 x) + 14.1

Intercambiar lados

2.3 sin (24 x) + 14.1 = 12.3

Multiplicar ambos lados por

10

2.3 sin (24 x) + 14.1 = 12.3

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

2.3 sin (24 x) \cdot 10 + 14.1 \cdot 10 = 12.3 \cdot 10

Simplificar

23 sin (24 x) + 141 = 123

23 sin (24 x) + 141 = 123

Mover

141

al lado derecho

23 sin (24 x) + 141 = 123

Restar

141

de ambos lados

23 sin (24 x) + 141 - 141 = 123 - 141

Simplificar

23 sin (24 x) = - 18

23 sin (24 x) = - 18

Dividir ambos lados entre

23

23 sin (24 x) = - 18

Dividir ambos lados entre

23

\frac{23 sin ( 24 x )}{23} = \frac{- 18}{23}

Simplificar

sin (24 x) = - \frac{18}{23}

sin (24 x) = - \frac{18}{23}

Aplicar propiedades trigonométricas inversas

sin (24 x) = - \frac{18}{23}

Soluciones generales para

sin (24 x) = - \frac{18}{23}

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

24 x = arcsin (- \frac{18}{23}) + 2 πn, 24 x = π + arcsin (\frac{18}{23}) + 2 πn

24 x = arcsin (- \frac{18}{23}) + 2 πn, 24 x = π + arcsin (\frac{18}{23}) + 2 πn

Resolver

24 x = arcsin (- \frac{18}{23}) + 2 πn : x = - \frac{arcsin ( \frac{18}{23} )}{24} + \frac{πn}{12}

24 x = arcsin (- \frac{18}{23}) + 2 πn

Simplificar

arcsin (- \frac{18}{23}) + 2 πn : - arcsin (\frac{18}{23}) + 2 πn

arcsin (- \frac{18}{23}) + 2 πn

Utilizar la siguiente propiedad:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{18}{23}) = - arcsin (\frac{18}{23})

= - arcsin (\frac{18}{23}) + 2 πn

24 x = - arcsin (\frac{18}{23}) + 2 πn

Dividir ambos lados entre

24

24 x = - arcsin (\frac{18}{23}) + 2 πn

Dividir ambos lados entre

24

\frac{24 x}{24} = - \frac{arcsin ( \frac{18}{23} )}{24} + \frac{2 πn}{24}

Simplificar

x = - \frac{arcsin ( \frac{18}{23} )}{24} + \frac{πn}{12}

x = - \frac{arcsin ( \frac{18}{23} )}{24} + \frac{πn}{12}

Resolver

24 x = π + arcsin (\frac{18}{23}) + 2 πn : x = \frac{π}{24} + \frac{arcsin ( \frac{18}{23} )}{24} + \frac{πn}{12}

24 x = π + arcsin (\frac{18}{23}) + 2 πn

Dividir ambos lados entre

24

24 x = π + arcsin (\frac{18}{23}) + 2 πn

Dividir ambos lados entre

24

\frac{24 x}{24} = \frac{π}{24} + \frac{arcsin ( \frac{18}{23} )}{24} + \frac{2 πn}{24}

Simplificar

x = \frac{π}{24} + \frac{arcsin ( \frac{18}{23} )}{24} + \frac{πn}{12}

x = \frac{π}{24} + \frac{arcsin ( \frac{18}{23} )}{24} + \frac{πn}{12}

x = - \frac{arcsin ( \frac{18}{23} )}{24} + \frac{πn}{12}, x = \frac{π}{24} + \frac{arcsin ( \frac{18}{23} )}{24} + \frac{πn}{12}

Mostrar soluciones en forma decimal

x = - \frac{0.89884 \dots}{24} + \frac{πn}{12}, x = \frac{π}{24} + \frac{0.89884 \dots}{24} + \frac{πn}{12}

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