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Popular >

sin(2x)-2cos(2x)=0

Solución

sin (2 x) - 2 cos (2 x) = 0

Solución

x = \frac{1.10714 \dots}{2} + \frac{πn}{2}

+1

Grados

x = 31.71747 \dots^{\circ} + 9 0^{\circ} n

Pasos de solución

sin (2 x) - 2 cos (2 x) = 0

Re-escribir usando identidades trigonométricas

sin (2 x) - 2 cos (2 x) = 0

Dividir ambos lados entre

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

\frac{sin ( 2 x ) - 2 cos ( 2 x )}{cos ( 2 x )} = \frac{0}{cos ( 2 x )}

Simplificar

\frac{sin ( 2 x )}{cos ( 2 x )} - 2 = 0

Utilizar la identidad trigonométrica básica:

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

tan (2 x) - 2 = 0

tan (2 x) - 2 = 0

Mover

2

al lado derecho

tan (2 x) - 2 = 0

Sumar

2

a ambos lados

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

Simplificar

tan (2 x) = 2

tan (2 x) = 2

Aplicar propiedades trigonométricas inversas

tan (2 x) = 2

Soluciones generales para

tan (2 x) = 2

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

2 x = arctan (2) + πn

2 x = arctan (2) + πn

Resolver

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

2 x = arctan (2) + πn

Dividir ambos lados entre

2

2 x = arctan (2) + πn

Dividir ambos lados entre

2

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

Simplificar

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

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

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

Mostrar soluciones en forma decimal

x = \frac{1.10714 \dots}{2} + \frac{πn}{2}

Ejemplos populares

tan(x)=(87.092)/(86.676)

tan (x) = \frac{87.092}{86.676}

csc (x) = - \frac{3}{2}

1 + 3 sin (θ) = 0

(tan(2x))/(sin(x))=-2

\frac{tan ( 2 x )}{sin ( x )} = - 2

sin (A) = 0.5