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Popular >

1/2 cot(x)=cos(x)

Solución

\frac{1}{2} cot (x) = cos (x)

Solución

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Grados

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n, x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n

Pasos de solución

\frac{1}{2} cot (x) = cos (x)

Restar

cos (x)

de ambos lados

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

Simplificar

\frac{1}{2} cot (x) - cos (x) : \frac{cot ( x ) - 2 cos ( x )}{2}

\frac{1}{2} cot (x) - cos (x)

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

\frac{1}{2} cot (x)

Multiplicar fracciones:

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

= \frac{1 \cdot cot ( x )}{2}

Multiplicar:

1 \cdot cot (x) = cot (x)

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

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

Convertir a fracción:

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

= \frac{cot ( x )}{2} - \frac{cos ( x ) \cdot 2}{2}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{cot ( x ) - cos ( x ) \cdot 2}{2}

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

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

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

Expresar con seno, coseno

cot (x) - 2 cos (x)

Utilizar la identidad trigonométrica básica:

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

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

Simplificar

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

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

Convertir a fracción:

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

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

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

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

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

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

Factorizar

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

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

Factorizar el termino común

- cos (x)

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

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

Resolver cada parte por separado

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

2 sin (x) - 1 = 0 : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

2 sin (x) - 1 = 0

Mover

1

al lado derecho

2 sin (x) - 1 = 0

Sumar

1

a ambos lados

2 sin (x) - 1 + 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

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

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

Soluciones generales para

sin (x) = \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}

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

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

Combinar toda las soluciones

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Ejemplos populares

solvefor θ,2cos(θ)+1=0 resolver para

θ, 2 cos (θ) + 1 = 0

-4+tan(θ)=(-12-sqrt(3))/3

- 4 + tan (θ) = \frac{- 12 - 3}{3}

2cos^2(x)-3=0

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

2sin(x)+sqrt(3)tan(x)=0

2 sin (x) + 3 tan (x) = 0

tan(t)=2,0<t< pi/2 ,cos(t)

tan (t) = 2, 0 < t < \frac{π}{2}, cos (t)