English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3cos(x)=sqrt(2)cot(x)

Solución

3 cos (x) = 2 cot (x)

Solución

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = 0.49088 \dots + 2 πn, x = π - 0.49088 \dots + 2 πn

Grados

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n, x = 28.12550 \dots^{\circ} + 36 0^{\circ} n, x = 151.87449 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

3 cos (x) = 2 cot (x)

Restar

2 cot (x)

de ambos lados

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

Expresar con seno, coseno

3 cos (x) - cot (x) 2

Utilizar la identidad trigonométrica básica:

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

= 3 cos (x) - \frac{cos ( x )}{sin ( x )} 2

Simplificar

3 cos (x) - \frac{cos ( x )}{sin ( x )} 2 : \frac{3 cos ( x ) sin ( x ) - 2 cos ( x )}{sin ( x )}

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

Multiplicar

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

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

Multiplicar fracciones:

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

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

= 3 cos (x) - \frac{2 cos ( x )}{sin ( x )}

Convertir a fracción:

3 cos (x) = \frac{3 cos ( x ) sin ( x )}{sin ( x )}

= \frac{3 cos ( x ) sin ( x )}{sin ( x )} - \frac{cos ( x ) 2}{sin ( x )}

Ya que los denominadores son iguales, combinar las fracciones:

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

= \frac{3 cos ( x ) sin ( x ) - cos ( x ) 2}{sin ( x )}

= \frac{3 cos ( x ) sin ( x ) - 2 cos ( x )}{sin ( x )}

\frac{- cos ( x ) 2 + 3 cos ( x ) sin ( x )}{sin ( x )} = 0

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

- cos (x) 2 + 3 cos (x) sin (x) = 0

Factorizar

- cos (x) 2 + 3 cos (x) sin (x) : cos (x) (- 2 + 3 sin (x))

- cos (x) 2 + 3 cos (x) sin (x)

Factorizar el termino común

cos (x)

= cos (x) (- 2 + 3 sin (x))

cos (x) (- 2 + 3 sin (x)) = 0

Resolver cada parte por separado

cos (x) = 0 or - 2 + 3 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

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

- 2 + 3 sin (x) = 0

Mover

2

al lado derecho

- 2 + 3 sin (x) = 0

Sumar

2

a ambos lados

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

Simplificar

3 sin (x) = 2

3 sin (x) = 2

Dividir ambos lados entre

3

3 sin (x) = 2

Dividir ambos lados entre

3

\frac{3 sin ( x )}{3} = \frac{2}{3}

Simplificar

sin (x) = \frac{2}{3}

sin (x) = \frac{2}{3}

Aplicar propiedades trigonométricas inversas

sin (x) = \frac{2}{3}

Soluciones generales para

sin (x) = \frac{2}{3}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{2}{3}) + 2 πn, x = π - arcsin (\frac{2}{3}) + 2 πn

x = arcsin (\frac{2}{3}) + 2 πn, x = π - arcsin (\frac{2}{3}) + 2 πn

Combinar toda las soluciones

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = arcsin (\frac{2}{3}) + 2 πn, x = π - arcsin (\frac{2}{3}) + 2 πn

Mostrar soluciones en forma decimal

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = 0.49088 \dots + 2 πn, x = π - 0.49088 \dots + 2 πn

Ejemplos populares

5cos(7θ)=0

5 cos (7 θ) = 0

-8tan(y)=0

- 8 tan (y) = 0

2cos^2(θ)+cos(θ)=0,0<= θ<2pi

2 cos^{2} (θ) + cos (θ) = 0, 0 \leq θ < 2 π

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

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

cos((-pi)/2+x/2)=0

cos (\frac{- π}{2} + \frac{x}{2}) = 0