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Popular >

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

Solución

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

Solución

x = 0.58800 \dots + πn

+1

Grados

x = 33.69006 \dots^{\circ} + 18 0^{\circ} n

Pasos de solución

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

Re-escribir usando identidades trigonométricas

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

Dividir ambos lados entre

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

\frac{\frac{s i n ( x )}{2}}{cos ( x )} = \frac{\frac{c o s ( x )}{3}}{cos ( x )}

Simplificar

\frac{sin ( x )}{2 cos ( x )} = \frac{1}{3}

Utilizar la identidad trigonométrica básica:

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

\frac{tan ( x )}{2} = \frac{1}{3}

\frac{tan ( x )}{2} = \frac{1}{3}

Multiplicar ambos lados por

2

\frac{tan ( x )}{2} = \frac{1}{3}

Multiplicar ambos lados por

2

\frac{2 tan ( x )}{2} = \frac{1 \cdot 2}{3}

Simplificar

\frac{2 tan ( x )}{2} = \frac{1 \cdot 2}{3}

Simplificar

\frac{2 tan ( x )}{2} : tan (x)

\frac{2 tan ( x )}{2}

Dividir:

\frac{2}{2} = 1

= tan (x)

Simplificar

\frac{1 \cdot 2}{3} : \frac{2}{3}

\frac{1 \cdot 2}{3}

Multiplicar los numeros:

1 \cdot 2 = 2

= \frac{2}{3}

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

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

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

Aplicar propiedades trigonométricas inversas

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

Soluciones generales para

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

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

x = arctan (\frac{2}{3}) + πn

x = arctan (\frac{2}{3}) + πn

Mostrar soluciones en forma decimal

x = 0.58800 \dots + πn

Ejemplos populares

4sin^2(θ)-2=0, pi/2 <θ<(3pi)/2

4 sin^{2} (θ) - 2 = 0, \frac{π}{2} < θ < \frac{3 π}{2}

9sin(x)+6cos(x)=10

9 sin (x) + 6 cos (x) = 10

-2cos^2(x)-sin(x)+1=0

- 2 cos^{2} (x) - sin (x) + 1 = 0

cos (x) = \frac{4}{21}

11-12cos^2(θ)=0

11 - 12 cos^{2} (θ) = 0