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sin(x)=(-(6))/((7)cos(x))

Solución

sin (x) = \frac{- ( 6 )}{( 7 ) cos ( x )}

Sin soluci \overset{o}{ˊ} n para x \in R

Pasos de solución

sin (x) = \frac{- ( 6 )}{( 7 ) cos ( x )}

Restar

\frac{- 6}{7 cos ( x )}

de ambos lados

sin (x) + \frac{6}{7 cos ( x )} = 0

Simplificar

sin (x) + \frac{6}{7 cos ( x )} : \frac{7 sin ( x ) cos ( x ) + 6}{7 cos ( x )}

sin (x) + \frac{6}{7 cos ( x )}

Convertir a fracción:

sin (x) = \frac{sin ( x ) 7 cos ( x )}{7 cos ( x )}

= \frac{sin ( x ) \cdot 7 cos ( x )}{7 cos ( x )} + \frac{6}{7 cos ( x )}

Ya que los denominadores son iguales, combinar las fracciones:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{sin ( x ) \cdot 7 cos ( x ) + 6}{7 cos ( x )}

\frac{7 sin ( x ) cos ( x ) + 6}{7 cos ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

7 sin (x) cos (x) + 6 = 0

Re-escribir usando identidades trigonométricas

7 sin (x) cos (x) + 6

Utilizar la identidad trigonométrica del ángulo doble:

2 sin (x) cos (x) = sin (2 x)

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

= 6 + 7 \cdot \frac{sin ( 2 x )}{2}

6 + 7 \cdot \frac{sin ( 2 x )}{2} = 0

Mover

6

al lado derecho

6 + 7 \cdot \frac{sin ( 2 x )}{2} = 0

Restar

6

de ambos lados

6 + 7 \cdot \frac{sin ( 2 x )}{2} - 6 = 0 - 6

Simplificar

7 \cdot \frac{sin ( 2 x )}{2} = - 6

7 \cdot \frac{sin ( 2 x )}{2} = - 6

Simplificar

7 \cdot \frac{sin ( 2 x )}{2} : \frac{7 sin ( 2 x )}{2}

7 \cdot \frac{sin ( 2 x )}{2}

Multiplicar fracciones:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{sin ( 2 x ) \cdot 7}{2}

\frac{7 sin ( 2 x )}{2} = - 6

Multiplicar ambos lados por

2

\frac{7 sin ( 2 x )}{2} = - 6

Multiplicar ambos lados por

2

\frac{7 sin ( 2 x )}{2} \cdot 2 = - 6 \cdot 2

Simplificar

\frac{7 sin ( 2 x )}{2} \cdot 2 = - 6 \cdot 2

Simplificar

\frac{7 sin ( 2 x )}{2} \cdot 2 : 7 sin (2 x)

\frac{7 sin ( 2 x )}{2} \cdot 2

Multiplicar fracciones:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{7 sin ( 2 x ) \cdot 2}{2}

Eliminar los terminos comunes:

2

= 7 sin (2 x)

Simplificar

- 6 \cdot 2 : - 12

- 6 \cdot 2

Multiplicar los numeros:

6 \cdot 2 = 12

= - 12

7 sin (2 x) = - 12

7 sin (2 x) = - 12

7 sin (2 x) = - 12

Dividir ambos lados entre

7

7 sin (2 x) = - 12

Dividir ambos lados entre

7

\frac{7 sin ( 2 x )}{7} = \frac{- 12}{7}

Simplificar

sin (2 x) = - \frac{12}{7}

sin (2 x) = - \frac{12}{7}

- 1 \leq sin (x) \leq 1

Sin soluci \overset{o}{ˊ} n para x \in R

5^{2} = 8^{2} - (11.85)^{2} - 2 (8) (11.85) (cos (A))

2 + 2 sin (θ) = 4

- 4 sin (8 x) = 0

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

\frac{sin ( θ )}{140} = \frac{sin ( 11 0 ^{\circ} )}{622}