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Popular >

2tan(θ)-sec(θ)=0

Solución

2 tan (θ) - sec (θ) = 0

Solución

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

+1

Grados

θ = 3 0^{\circ} + 36 0^{\circ} n, θ = 15 0^{\circ} + 36 0^{\circ} n

Pasos de solución

2 tan (θ) - sec (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 \cdot \frac{sin ( θ )}{cos ( θ )}

Simplificar

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

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

Multiplicar

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

2 \cdot \frac{sin ( θ )}{cos ( θ )}

Multiplicar fracciones:

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

= \frac{sin ( θ ) \cdot 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 + 2 sin ( θ )}{cos ( θ )} = 0

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

- 1 + 2 sin (θ) = 0

Mover

1

al lado derecho

- 1 + 2 sin (θ) = 0

Sumar

1

a ambos lados

- 1 + 2 sin (θ) + 1 = 0 + 1

Simplificar

2 sin (θ) = 1

2 sin (θ) = 1

Dividir ambos lados entre

2

2 sin (θ) = 1

Dividir ambos lados entre

2

\frac{2 sin ( θ )}{2} = \frac{1}{2}

Simplificar

sin (θ) = \frac{1}{2}

sin (θ) = \frac{1}{2}

Soluciones generales para

sin (θ) = \frac{1}{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}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Ejemplos populares

sin(θ)= 175/214

sin (θ) = \frac{175}{214}

2*cos^2(x)-cos(x)-1=0,0<= x<= pi

2 \cdot cos^{2} (x) - cos (x) - 1 = 0, 0 \leq x \leq π

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

2 cos^{3} (x) - cos^{2} (x) = 0

sin^2(x)-2=sin(x)

sin^{2} (x) - 2 = sin (x)

arccosh(x)=(2pi)/7

arccosh (x) = \frac{2 π}{7}