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Popular >

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

Solución

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

Solución

x = \frac{0.54041 \dots}{2} + \frac{πn}{2}

+1

Grados

x = 15.48187 \dots^{\circ} + 9 0^{\circ} n

Pasos de solución

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

Re-escribir usando identidades trigonométricas

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

Dividir ambos lados entre

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

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

Simplificar

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

Utilizar la identidad trigonométrica básica:

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

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) + πn

2 x = arctan (\frac{3}{5}) + πn

2 x = arctan (\frac{3}{5}) + πn

Resolver

2 x = arctan (\frac{3}{5}) + πn : x = \frac{arctan ( \frac{3}{5} )}{2} + \frac{πn}{2}

2 x = arctan (\frac{3}{5}) + πn

Dividir ambos lados entre

2

2 x = arctan (\frac{3}{5}) + πn

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{arctan ( \frac{3}{5} )}{2} + \frac{πn}{2}

Simplificar

x = \frac{arctan ( \frac{3}{5} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{3}{5} )}{2} + \frac{πn}{2}

x = \frac{arctan ( \frac{3}{5} )}{2} + \frac{πn}{2}

Mostrar soluciones en forma decimal

x = \frac{0.54041 \dots}{2} + \frac{πn}{2}

Ejemplos populares

4 cos (3 x - 20) = 1

0=1.9cos(0.1t)-1.25sin(0.2t)

0 = 1.9 cos (0.1 t) - 1.25 sin (0.2 t)

sin(x/4)=(sqrt(3))/2

sin (\frac{x}{4}) = \frac{3}{2}

cos(θ)=(-3+(-6))/((sqrt(9))(\sqrt{18))}

cos (θ) = \frac{- 3 + ( - 6 )}{( 9 ) ( 18 )}

sin (\frac{6}{x}) = 36