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Popular Trigonometría >

sec(x)cot(x)= 7/6

Solución

sec (x) cot (x) = \frac{7}{6}

Solución

x = 1.02969 \dots + 2 πn, x = π - 1.02969 \dots + 2 πn

Grados

x = 58.99728 \dots^{\circ} + 36 0^{\circ} n, x = 121.00271 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

sec (x) cot (x) = \frac{7}{6}

Restar

\frac{7}{6}

de ambos lados

sec (x) cot (x) - \frac{7}{6} = 0

Simplificar

sec (x) cot (x) - \frac{7}{6} : \frac{6 sec ( x ) cot ( x ) - 7}{6}

sec (x) cot (x) - \frac{7}{6}

Convertir a fracción:

sec (x) cot (x) = \frac{sec ( x ) cot ( x ) 6}{6}

= \frac{sec ( x ) cot ( x ) \cdot 6}{6} - \frac{7}{6}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{sec ( x ) cot ( x ) \cdot 6 - 7}{6}

\frac{6 sec ( x ) cot ( x ) - 7}{6} = 0

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

6 sec (x) cot (x) - 7 = 0

Expresar con seno, coseno

- 7 + 6 cot (x) sec (x)

Utilizar la identidad trigonométrica básica:

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

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

Utilizar la identidad trigonométrica básica:

sec (x) = \frac{1}{cos ( x )}

= - 7 + 6 \cdot \frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )}

Simplificar

- 7 + 6 \cdot \frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )} : \frac{- 7 sin ( x ) + 6}{sin ( x )}

- 7 + 6 \cdot \frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )}

6 \cdot \frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )} = \frac{6}{sin ( x )}

6 \cdot \frac{cos ( x )}{sin ( x )} \cdot \frac{1}{cos ( x )}

Multiplicar fracciones:

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

= \frac{cos ( x ) \cdot 1 \cdot 6}{sin ( x ) cos ( x )}

Eliminar los terminos comunes:

cos (x)

= \frac{1 \cdot 6}{sin ( x )}

Multiplicar los numeros:

1 \cdot 6 = 6

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

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

Convertir a fracción:

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

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

Ya que los denominadores son iguales, combinar las fracciones:

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

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

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

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

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

6 - 7 sin (x) = 0

Desplace

6

a la derecha

6 - 7 sin (x) = 0

Restar

6

de ambos lados

6 - 7 sin (x) - 6 = 0 - 6

Simplificar

- 7 sin (x) = - 6

- 7 sin (x) = - 6

Dividir ambos lados entre

- 7

- 7 sin (x) = - 6

Dividir ambos lados entre

- 7

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

Simplificar

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

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

Aplicar propiedades trigonométricas inversas

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

Soluciones generales para

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

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{6}{7}) + 2 πn, x = π - arcsin (\frac{6}{7}) + 2 πn

x = arcsin (\frac{6}{7}) + 2 πn, x = π - arcsin (\frac{6}{7}) + 2 πn

Mostrar soluciones en forma decimal

x = 1.02969 \dots + 2 πn, x = π - 1.02969 \dots + 2 πn

Gráfica

Ejemplos populares

sin^2(x)-3sin(x)cos(x)+2cos^2(x)=0