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Popular >

tan^2(θ)=(sin^2(θ))/(cos(θ))

Solución

tan^{2} (θ) = \frac{sin ^{2} ( θ )}{cos ( θ )}

Solución

θ = 2 πn, θ = π + 2 πn

Grados

θ = 0^{\circ} + 36 0^{\circ} n, θ = 18 0^{\circ} + 36 0^{\circ} n

Pasos de solución

tan^{2} (θ) = \frac{sin ^{2} ( θ )}{cos ( θ )}

Restar

\frac{sin ^{2} ( θ )}{cos ( θ )}

de ambos lados

tan^{2} (θ) - \frac{sin ^{2} ( θ )}{cos ( θ )} = 0

Simplificar

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

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

Convertir a fracción:

tan^{2} (θ) = \frac{tan ^{2} ( θ ) cos ( θ )}{cos ( θ )}

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

Ya que los denominadores son iguales, combinar las fracciones:

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

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

\frac{tan ^{2} ( θ ) cos ( θ ) - sin ^{2} ( θ )}{cos ( θ )} = 0

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

tan^{2} (θ) cos (θ) - sin^{2} (θ) = 0

Expresar con seno, coseno

- sin^{2} (θ) + cos (θ) tan^{2} (θ)

Utilizar la identidad trigonométrica básica:

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

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

Simplificar

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

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

cos (θ) (\frac{sin ( θ )}{cos ( θ )})^{2} = \frac{sin ^{2} ( θ )}{cos ( θ )}

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

(\frac{sin ( θ )}{cos ( θ )})^{2} = \frac{sin ^{2} ( θ )}{cos ^{2} ( θ )}

(\frac{sin ( θ )}{cos ( θ )})^{2}

Aplicar las leyes de los exponentes:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{sin ^{2} ( θ )}{cos ^{2} ( θ )}

= \frac{sin ^{2} ( θ )}{cos ^{2} ( θ )} cos (θ)

Multiplicar fracciones:

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

= \frac{sin ^{2} ( θ ) cos ( θ )}{cos ^{2} ( θ )}

Eliminar los terminos comunes:

cos (θ)

= \frac{sin ^{2} ( θ )}{cos ( θ )}

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

Convertir a fracción:

sin^{2} (θ) = \frac{sin ^{2} ( θ ) cos ( θ )}{cos ( θ )}

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

Ya que los denominadores son iguales, combinar las fracciones:

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

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

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

\frac{sin ^{2} ( θ ) - cos ( θ ) sin ^{2} ( θ )}{cos ( θ )} = 0

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

sin^{2} (θ) - cos (θ) sin^{2} (θ) = 0

Factorizar

sin^{2} (θ) - cos (θ) sin^{2} (θ) : - sin^{2} (θ) (cos (θ) - 1)

sin^{2} (θ) - cos (θ) sin^{2} (θ)

Factorizar el termino común

- sin^{2} (θ)

= - sin^{2} (θ) (- 1 + cos (θ))

- sin^{2} (θ) (cos (θ) - 1) = 0

Resolver cada parte por separado

sin^{2} (θ) = 0 or cos (θ) - 1 = 0

sin^{2} (θ) = 0 : θ = 2 πn, θ = π + 2 πn

sin^{2} (θ) = 0

Aplicar la regla

x^{n} = 0 \Rightarrow x = 0

sin (θ) = 0

Soluciones generales para

sin (θ) = 0

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 = 0 + 2 πn, θ = π + 2 πn

θ = 0 + 2 πn, θ = π + 2 πn

Resolver

θ = 0 + 2 πn : θ = 2 πn

θ = 0 + 2 πn

0 + 2 πn = 2 πn

θ = 2 πn

θ = 2 πn, θ = π + 2 πn

cos (θ) - 1 = 0 : θ = 2 πn

cos (θ) - 1 = 0

Mover

1

al lado derecho

cos (θ) - 1 = 0

Sumar

1

a ambos lados

cos (θ) - 1 + 1 = 0 + 1

Simplificar

cos (θ) = 1

cos (θ) = 1

Soluciones generales para

cos (θ) = 1

cos (x)

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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

θ = 0 + 2 πn

θ = 0 + 2 πn

Resolver

θ = 0 + 2 πn : θ = 2 πn

θ = 0 + 2 πn

0 + 2 πn = 2 πn

θ = 2 πn

θ = 2 πn

Combinar toda las soluciones

θ = 2 πn, θ = π + 2 πn

Ejemplos populares

tan(x)=1,17

tan (x) = 1, 17

solvefor θ,2cot(θ)-1=0 resolver para

θ, 2 cot (θ) - 1 = 0

cos(x)= a/b

cos (x) = \frac{a}{b}

sin^2(θ)-sin(θ)-12=0

sin^{2} (θ) - sin (θ) - 12 = 0

2cos^2(x)-sin(-x)-1=0

2 cos^{2} (x) - sin (- x) - 1 = 0