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Popular >

sin(2x)=-5cos(2x),0<= x<= 2pi

Solución

sin (2 x) = - 5 cos (2 x), 0 \leq x \leq 2 π

Solución

x = \frac{- 1.37340 \dots + π}{2}, x = \frac{- 1.37340 \dots + 2 π}{2}, x = \frac{- 1.37340 \dots + 3 π}{2}, x = \frac{- 1.37340 \dots + 4 π}{2}

+1

Grados

x = 50.65496 \dots^{\circ}, x = 140.65496 \dots^{\circ}, x = 230.65496 \dots^{\circ}, x = 320.65496 \dots^{\circ}

Pasos de solución

sin (2 x) = - 5 cos (2 x), 0 \leq x \leq 2 π

Re-escribir usando identidades trigonométricas

sin (2 x) = - 5 cos (2 x)

Dividir ambos lados entre

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

\frac{sin ( 2 x )}{cos ( 2 x )} = \frac{- 5 cos ( 2 x )}{cos ( 2 x )}

Simplificar

\frac{sin ( 2 x )}{cos ( 2 x )} = - 5

Utilizar la identidad trigonométrica básica:

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

tan (2 x) = - 5

tan (2 x) = - 5

Aplicar propiedades trigonométricas inversas

tan (2 x) = - 5

Soluciones generales para

tan (2 x) = - 5

tan (x) = - a \Rightarrow x = arctan (- a) + πn

2 x = arctan (- 5) + πn

2 x = arctan (- 5) + πn

Resolver

2 x = arctan (- 5) + πn : x = - \frac{arctan ( 5 )}{2} + \frac{πn}{2}

2 x = arctan (- 5) + πn

Simplificar

arctan (- 5) + πn : - arctan (5) + πn

arctan (- 5) + πn

Utilizar la siguiente propiedad:

arctan (- x) = - arctan (x)

arctan (- 5) = - arctan (5)

= - arctan (5) + πn

2 x = - arctan (5) + πn

Dividir ambos lados entre

2

2 x = - arctan (5) + πn

Dividir ambos lados entre

2

\frac{2 x}{2} = - \frac{arctan ( 5 )}{2} + \frac{πn}{2}

Simplificar

x = - \frac{arctan ( 5 )}{2} + \frac{πn}{2}

x = - \frac{arctan ( 5 )}{2} + \frac{πn}{2}

x = - \frac{arctan ( 5 )}{2} + \frac{πn}{2}

Soluciones para el rango

0 \leq x \leq 2 π

x = \frac{- arctan ( 5 ) + π}{2}, x = \frac{- arctan ( 5 ) + 2 π}{2}, x = \frac{- arctan ( 5 ) + 3 π}{2}, x = \frac{- arctan ( 5 ) + 4 π}{2}

Mostrar soluciones en forma decimal

x = \frac{- 1.37340 \dots + π}{2}, x = \frac{- 1.37340 \dots + 2 π}{2}, x = \frac{- 1.37340 \dots + 3 π}{2}, x = \frac{- 1.37340 \dots + 4 π}{2}

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2cos^2(x)+9cos(x)-5=0

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cos(θ)=-(sqrt(3))/4

cos (θ) = - \frac{3}{4}

tan(θ)=(sqrt(3))/2

tan (θ) = \frac{3}{2}

5 sin (θ) + 7 = 0

5sin(x)tan(x)+4tan(x)=0

5 sin (x) tan (x) + 4 tan (x) = 0