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Popular >

(sin(x))/(tan(x))=-0.375

Solución

\frac{sin ( x )}{tan ( x )} = - 0.375

Solución

x = 1.95519 \dots + 2 πn, x = - 1.95519 \dots + 2 πn

+1

Grados

x = 112.02431 \dots^{\circ} + 36 0^{\circ} n, x = - 112.02431 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

\frac{sin ( x )}{tan ( x )} = - 0.375

Restar

- 0.375

de ambos lados

\frac{sin ( x )}{tan ( x )} + 0.375 = 0

Re-escribir usando identidades trigonométricas

0.375 + \frac{sin ( x )}{tan ( x )}

Utilizar la identidad trigonométrica básica:

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

= 0.375 + \frac{sin ( x )}{\frac{s i n ( x )}{c o s ( x )}}

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

\frac{sin ( x )}{\frac{s i n ( x )}{c o s ( x )}}

Aplicar las propiedades de las fracciones:

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

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

Eliminar los terminos comunes:

sin (x)

= cos (x)

= 0.375 + cos (x)

0.375 + cos (x) = 0

Mover

0.375

al lado derecho

0.375 + cos (x) = 0

Restar

0.375

de ambos lados

0.375 + cos (x) - 0.375 = 0 - 0.375

Simplificar

cos (x) = - 0.375

cos (x) = - 0.375

Aplicar propiedades trigonométricas inversas

cos (x) = - 0.375

Soluciones generales para

cos (x) = - 0.375

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

x = arccos (- 0.375) + 2 πn, x = - arccos (- 0.375) + 2 πn

x = arccos (- 0.375) + 2 πn, x = - arccos (- 0.375) + 2 πn

Mostrar soluciones en forma decimal

x = 1.95519 \dots + 2 πn, x = - 1.95519 \dots + 2 πn

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