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Popular >

sin(θ-pi)=-1/(sqrt(2))

Solución

sin (θ - π) = - \frac{1}{2}

Solución

θ = \frac{5 π}{4} + 2 πn + π, θ = \frac{7 π}{4} + 2 πn + π

+1

radianes

θ = \frac{5 π}{4} + π + 2 πn, θ = \frac{7 π}{4} + π + 2 πn

Pasos de solución

sin (θ - π) = - \frac{1}{2}

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 (θ - π) = - \frac{2}{2}

Soluciones generales para

sin (θ - π) = - \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}

θ - π = \frac{5 π}{4} + 2 πn, θ - π = \frac{7 π}{4} + 2 πn

θ - π = \frac{5 π}{4} + 2 πn, θ - π = \frac{7 π}{4} + 2 πn

Resolver

θ - π = \frac{5 π}{4} + 2 πn : θ = \frac{5 π}{4} + 2 πn + π

θ - π = \frac{5 π}{4} + 2 πn

Mover

π

al lado derecho

θ - π = \frac{5 π}{4} + 2 πn

Sumar

π

a ambos lados

θ - π + π = \frac{5 π}{4} + 2 πn + π

Simplificar

θ = \frac{5 π}{4} + 2 πn + π

θ = \frac{5 π}{4} + 2 πn + π

Resolver

θ - π = \frac{7 π}{4} + 2 πn : θ = \frac{7 π}{4} + 2 πn + π

θ - π = \frac{7 π}{4} + 2 πn

Mover

π

al lado derecho

θ - π = \frac{7 π}{4} + 2 πn

Sumar

π

a ambos lados

θ - π + π = \frac{7 π}{4} + 2 πn + π

Simplificar

θ = \frac{7 π}{4} + 2 πn + π

θ = \frac{7 π}{4} + 2 πn + π

θ = \frac{5 π}{4} + 2 πn + π, θ = \frac{7 π}{4} + 2 πn + π

Ejemplos populares

7-2sin(5(x+pi/8))=9

7 - 2 sin (5 (x + \frac{π}{8})) = 9

solvefor x,4cos^2(x)=3 resolver para

x, 4 cos^{2} (x) = 3

sin(2x)+(sqrt(2))/2 =0

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

cos(θ)-sin(θ)=sqrt(2)

cos (θ) - sin (θ) = 2

3sin(2x+30)=tan(2x+30)

3 sin (2 x + 30) = tan (2 x + 30)