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Popular >

sec(θ)-sqrt(2)tan(θ)=0

Solución

sec (θ) - 2 tan (θ) = 0

Solución

θ = \frac{π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn

+1

Grados

θ = 4 5^{\circ} + 36 0^{\circ} n, θ = 13 5^{\circ} + 36 0^{\circ} n

Pasos de solución

sec (θ) - 2 tan (θ) = 0

Expresar con seno, coseno

sec (θ) - 2 tan (θ)

Utilizar la identidad trigonométrica básica:

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

= \frac{1}{cos ( θ )} - 2 tan (θ)

Utilizar la identidad trigonométrica básica:

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

= \frac{1}{cos ( θ )} - 2 \frac{sin ( θ )}{cos ( θ )}

Simplificar

\frac{1}{cos ( θ )} - 2 \frac{sin ( θ )}{cos ( θ )} : \frac{1 - 2 sin ( θ )}{cos ( θ )}

\frac{1}{cos ( θ )} - 2 \frac{sin ( θ )}{cos ( θ )}

Multiplicar

2 \frac{sin ( θ )}{cos ( θ )} : \frac{2 sin ( θ )}{cos ( θ )}

2 \frac{sin ( θ )}{cos ( θ )}

Multiplicar fracciones:

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

= \frac{sin ( θ ) 2}{cos ( θ )}

= \frac{1}{cos ( θ )} - \frac{2 sin ( θ )}{cos ( θ )}

Aplicar la regla

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

= \frac{1 - 2 sin ( θ )}{cos ( θ )}

= \frac{1 - 2 sin ( θ )}{cos ( θ )}

\frac{1 - sin ( θ ) 2}{cos ( θ )} = 0

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

1 - sin (θ) 2 = 0

Mover

1

al lado derecho

1 - sin (θ) 2 = 0

Restar

1

de ambos lados

1 - sin (θ) 2 - 1 = 0 - 1

Simplificar

- sin (θ) 2 = - 1

- sin (θ) 2 = - 1

Dividir ambos lados entre

- 2

- sin (θ) 2 = - 1

Dividir ambos lados entre

- 2

\frac{- sin ( θ ) 2}{- 2} = \frac{- 1}{- 2}

Simplificar

\frac{- sin ( θ ) 2}{- 2} = \frac{- 1}{- 2}

Simplificar

\frac{- sin ( θ ) 2}{- 2} : sin (θ)

\frac{- sin ( θ ) 2}{- 2}

Aplicar las propiedades de las fracciones:

\frac{- a}{- b} = \frac{a}{b}

= \frac{sin ( θ ) 2}{2}

Eliminar los terminos comunes:

2

= sin (θ)

Simplificar

\frac{- 1}{- 2} : \frac{2}{2}

\frac{- 1}{- 2}

Aplicar las propiedades de las fracciones:

\frac{- a}{- b} = \frac{a}{b}

= \frac{1}{2}

Racionalizar

\frac{1}{2} : \frac{2}{2}

\frac{1}{2}

Multiplicar por el conjugado

\frac{2}{2}

= \frac{1 \cdot 2}{2 2}

1 \cdot 2 = 2

22 = 2

22

Aplicar las leyes de los exponentes:

a a = a

22 = 2

= 2

= \frac{2}{2}

= \frac{2}{2}

sin (θ) = \frac{2}{2}

sin (θ) = \frac{2}{2}

sin (θ) = \frac{2}{2}

Soluciones generales para

sin (θ) = \frac{2}{2}

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}

θ = \frac{π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn

θ = \frac{π}{4} + 2 πn, θ = \frac{3 π}{4} + 2 πn

Ejemplos populares

2sin(θ)cos(θ)+sqrt(3)cos(θ)=0

2 sin (θ) cos (θ) + 3 cos (θ) = 0

2sin(x-pi/3)=-sqrt(2)

2 sin (x - \frac{π}{3}) = - 2

3cos^2(x)+2cos(x)=1

3 cos^{2} (x) + 2 cos (x) = 1

3sin(θ)=1+cos(θ)

3 sin (θ) = 1 + cos (θ)

sqrt(2)sin(x)-sqrt(2)cos(x)=2

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