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Popular >

cos(x)(4sin(x)+1)=0

Solución

cos (x) (4 sin (x) + 1) = 0

Solución

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = - 0.25268 \dots + 2 πn, x = π + 0.25268 \dots + 2 πn

+1

Grados

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n, x = - 14.47751 \dots^{\circ} + 36 0^{\circ} n, x = 194.47751 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

cos (x) (4 sin (x) + 1) = 0

Resolver cada parte por separado

cos (x) = 0 or 4 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

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

4 sin (x) + 1 = 0

Mover

1

al lado derecho

4 sin (x) + 1 = 0

Restar

1

de ambos lados

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

Simplificar

4 sin (x) = - 1

4 sin (x) = - 1

Dividir ambos lados entre

4

4 sin (x) = - 1

Dividir ambos lados entre

4

\frac{4 sin ( x )}{4} = \frac{- 1}{4}

Simplificar

sin (x) = - \frac{1}{4}

sin (x) = - \frac{1}{4}

Aplicar propiedades trigonométricas inversas

sin (x) = - \frac{1}{4}

Soluciones generales para

sin (x) = - \frac{1}{4}

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

x = arcsin (- \frac{1}{4}) + 2 πn, x = π + arcsin (\frac{1}{4}) + 2 πn

x = arcsin (- \frac{1}{4}) + 2 πn, x = π + arcsin (\frac{1}{4}) + 2 πn

Combinar toda las soluciones

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

Mostrar soluciones en forma decimal

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = - 0.25268 \dots + 2 πn, x = π + 0.25268 \dots + 2 πn

Ejemplos populares

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

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

cos(φ)=sin(φ)

cos (φ) = sin (φ)

cos(x-pi/(13))=-1

cos (x - \frac{π}{13}) = - 1

cos(x)=sqrt(2)-cos(x)

cos (x) = 2 - cos (x)

solvefor θ,ρ=sin(θ)sin(φ)resolver para

θ, ρ = sin (θ) sin (φ)