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Popular >

sqrt(2)cos(x)=cot(x)

Solución

2 cos (x) = cot (x)

Solución

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

Grados

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n, x = 4 5^{\circ} + 36 0^{\circ} n, x = 13 5^{\circ} + 36 0^{\circ} n

Pasos de solución

2 cos (x) = cot (x)

Restar

cot (x)

de ambos lados

2 cos (x) - cot (x) = 0

Expresar con seno, coseno

- cot (x) + cos (x) 2

Utilizar la identidad trigonométrica básica:

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

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

Simplificar

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

- \frac{cos ( x )}{sin ( x )} + cos (x) 2

Convertir a fracción:

2 cos (x) = \frac{cos ( x ) 2 sin ( x )}{sin ( x )}

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

Ya que los denominadores son iguales, combinar las fracciones:

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

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

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

\frac{- cos ( x ) + cos ( x ) sin ( x ) 2}{sin ( x )} = 0

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

- cos (x) + cos (x) sin (x) 2 = 0

Factorizar

- cos (x) + cos (x) sin (x) 2 : cos (x) (- 1 + 2 sin (x))

- cos (x) + cos (x) sin (x) 2

Factorizar el termino común

cos (x)

= cos (x) (- 1 + sin (x) 2)

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

Resolver cada parte por separado

cos (x) = 0 or - 1 + 2 sin (x) = 0

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = 0

Soluciones generales para

cos (x) = 0

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}

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

- 1 + 2 sin (x) = 0 : x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn

- 1 + 2 sin (x) = 0

Mover

1

al lado derecho

- 1 + 2 sin (x) = 0

Sumar

1

a ambos lados

- 1 + 2 sin (x) + 1 = 0 + 1

Simplificar

2 sin (x) = 1

2 sin (x) = 1

Dividir ambos lados entre

2

2 sin (x) = 1

Dividir ambos lados entre

2

\frac{2 sin ( x )}{2} = \frac{1}{2}

Simplificar

\frac{2 sin ( x )}{2} = \frac{1}{2}

Simplificar

\frac{2 sin ( x )}{2} : sin (x)

\frac{2 sin ( x )}{2}

Eliminar los terminos comunes:

2

= sin (x)

Simplificar

\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}

sin (x) = \frac{2}{2}

sin (x) = \frac{2}{2}

sin (x) = \frac{2}{2}

Soluciones generales para

sin (x) = \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}

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

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

Combinar toda las soluciones

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

Ejemplos populares

tan(x)=(60}{\frac{(-20-90))/2}

tan (x) = \frac{60}{\frac{( - 20 - 90 )}{2}}

0.1*sin(θ)cos(53.13)+0.1*sin(θ)=0

0.1 \cdot sin (θ) cos (53.1 3^{\circ}) + 0.1 \cdot sin (θ) = 0

tan(θ)=(1)

tan (θ) = (1)

sec^2(x)=(3sqrt(3))/pi

sec^{2} (x) = \frac{3 3}{π}

sin(θ)(sin(θ)+1)=0

sin (θ) (sin (θ) + 1) = 0