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Popular Trigonometría >

5sin(2x)+3cos(2x)=0,0<= x<= 180

Solución

5 sin (2 x) + 3 cos (2 x) = 0, 0^{\circ} \leq x \leq 18 0^{\circ}

Solución

x = \frac{- 0.54041 \dots + 18 0 ^{\circ}}{2}, x = \frac{- 0.54041 \dots + 36 0 ^{\circ}}{2}

+1

Radianes

x = \frac{- 0.54041 \dots + π}{2}, x = \frac{- 0.54041 \dots + 2 π}{2}

Pasos de solución

5 sin (2 x) + 3 cos (2 x) = 0, 0^{\circ} \leq x \leq 18 0^{\circ}

Re-escribir usando identidades trigonométricas

5 sin (2 x) + 3 cos (2 x) = 0

Dividir ambos lados entre

cos (2 x), cos (2 x) \neq = 0

\frac{5 sin ( 2 x ) + 3 cos ( 2 x )}{cos ( 2 x )} = \frac{0}{cos ( 2 x )}

Simplificar

\frac{5 sin ( 2 x )}{cos ( 2 x )} + 3 = 0

Utilizar la identidad trigonométrica básica:

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

5 tan (2 x) + 3 = 0

5 tan (2 x) + 3 = 0

Desplace

3

a la derecha

5 tan (2 x) + 3 = 0

Restar

3

de ambos lados

5 tan (2 x) + 3 - 3 = 0 - 3

Simplificar

5 tan (2 x) = - 3

5 tan (2 x) = - 3

Dividir ambos lados entre

5

5 tan (2 x) = - 3

Dividir ambos lados entre

5

\frac{5 tan ( 2 x )}{5} = \frac{- 3}{5}

Simplificar

tan (2 x) = - \frac{3}{5}

tan (2 x) = - \frac{3}{5}

Aplicar propiedades trigonométricas inversas

tan (2 x) = - \frac{3}{5}

Soluciones generales para

tan (2 x) = - \frac{3}{5}

tan (x) = - a \Rightarrow x = arctan (- a) + 18 0^{\circ} n

2 x = arctan (- \frac{3}{5}) + 18 0^{\circ} n

2 x = arctan (- \frac{3}{5}) + 18 0^{\circ} n

Resolver

2 x = arctan (- \frac{3}{5}) + 18 0^{\circ} n : x = - \frac{arctan ( \frac{3}{5} )}{2} + \frac{18 0 ^{\circ} n}{2}

2 x = arctan (- \frac{3}{5}) + 18 0^{\circ} n

Simplificar

arctan (- \frac{3}{5}) + 18 0^{\circ} n : - arctan (\frac{3}{5}) + 18 0^{\circ} n

arctan (- \frac{3}{5}) + 18 0^{\circ} n

Utilizar la siguiente propiedad:

arctan (- x) = - arctan (x)

arctan (- \frac{3}{5}) = - arctan (\frac{3}{5})

= - arctan (\frac{3}{5}) + 18 0^{\circ} n

2 x = - arctan (\frac{3}{5}) + 18 0^{\circ} n

Dividir ambos lados entre

2

2 x = - arctan (\frac{3}{5}) + 18 0^{\circ} n

Dividir ambos lados entre

2

\frac{2 x}{2} = - \frac{arctan ( \frac{3}{5} )}{2} + \frac{18 0 ^{\circ} n}{2}

Simplificar

x = - \frac{arctan ( \frac{3}{5} )}{2} + \frac{18 0 ^{\circ} n}{2}

x = - \frac{arctan ( \frac{3}{5} )}{2} + \frac{18 0 ^{\circ} n}{2}

x = - \frac{arctan ( \frac{3}{5} )}{2} + \frac{18 0 ^{\circ} n}{2}

Soluciones para el rango

0 \leq x \leq 18 0^{\circ}

x = \frac{- arctan ( \frac{3}{5} ) + 18 0 ^{\circ}}{2}, x = \frac{- arctan ( \frac{3}{5} ) + 36 0 ^{\circ}}{2}

Mostrar soluciones en forma decimal

x = \frac{- 0.54041 \dots + 18 0 ^{\circ}}{2}, x = \frac{- 0.54041 \dots + 36 0 ^{\circ}}{2}

Gráfica

Ejemplos populares

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