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sec(x)=(sin(x))/(cos(x))

Solución

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

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

Pasos de solución

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

Restar

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

de ambos lados

sec (x) - \frac{sin ( x )}{cos ( x )} = 0

Simplificar

sec (x) - \frac{sin ( x )}{cos ( x )} : \frac{sec ( x ) cos ( x ) - sin ( x )}{cos ( x )}

sec (x) - \frac{sin ( x )}{cos ( x )}

Convertir a fracción:

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

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

Ya que los denominadores son iguales, combinar las fracciones:

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

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

\frac{sec ( x ) cos ( x ) - sin ( x )}{cos ( x )} = 0

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

sec (x) cos (x) - sin (x) = 0

Re-escribir usando identidades trigonométricas

sec (x) cos (x) - sin (x)

sec (x) cos (x) = 1

sec (x) cos (x)

Expresar con seno, coseno

sec (x) cos (x)

Utilizar la identidad trigonométrica básica:

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

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

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

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

Multiplicar fracciones:

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

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

Eliminar los terminos comunes:

cos (x)

= 1

= 1

= - sin (x) + 1

- sin (x) + 1 = 0

Mover

1

al lado derecho

- sin (x) + 1 = 0

Restar

1

de ambos lados

- sin (x) + 1 - 1 = 0 - 1

Simplificar

- sin (x) = - 1

- sin (x) = - 1

Dividir ambos lados entre

- 1

- sin (x) = - 1

Dividir ambos lados entre

- 1

\frac{- sin ( x )}{- 1} = \frac{- 1}{- 1}

Simplificar

sin (x) = 1

sin (x) = 1

Soluciones generales para

sin (x) = 1

tabla de valores periódicos con

2 πn

intervalos:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

Siendo que la ecuación esta indefinida para:

\frac{π}{2} + 2 πn

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

- cos (20.02 t) = sin (20 t)

sin^{3} (x) + 3 sin^{2} (x) + 2 sin (x) = 0, 0 \leq x < 2 π

sin (2 x - \frac{π}{6}) = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

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

b, a = arccos (\frac{a ^{2} - b ^{2} - c ^{2}}{- 2 b c})