English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(x)-cos(x)=0.5

Solución

sin (x) - cos (x) = 0.5

Solución

x = 0.36136 \dots + 2 πn + \frac{π}{4}, x = π - 0.36136 \dots + 2 πn + \frac{π}{4}

Grados

x = 65.70481 \dots^{\circ} + 36 0^{\circ} n, x = 204.29518 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

sin (x) - cos (x) = 0.5

Re-escribir usando identidades trigonométricas

sin (x) - cos (x)

sin (x) - cos (x) = 2 sin (x - \frac{π}{4})

sin (x) - cos (x)

Reescribir como

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

Utilizar la siguiente identidad trivial:

cos (\frac{π}{4}) = \frac{1}{2}

Utilizar la siguiente identidad trivial:

sin (\frac{π}{4}) = \frac{1}{2}

= 2 (cos (\frac{π}{4}) sin (x) - sin (\frac{π}{4}) cos (x))

Utilizar la identidad de suma de ángulos:

sin (s - t) = sin (s) cos (t) - cos (s) sin (t)

= 2 sin (x - \frac{π}{4})

= 2 sin (x - \frac{π}{4})

2 sin (x - \frac{π}{4}) = 0.5

Dividir ambos lados entre

2

2 sin (x - \frac{π}{4}) = 0.5

Dividir ambos lados entre

2

\frac{2 sin ( x - \frac{π}{4} )}{2} = \frac{0.5}{2}

Simplificar

\frac{2 sin ( x - \frac{π}{4} )}{2} = \frac{0.5}{2}

Simplificar

\frac{2 sin ( x - \frac{π}{4} )}{2} : sin (x - \frac{π}{4})

\frac{2 sin ( x - \frac{π}{4} )}{2}

Eliminar los terminos comunes:

2

= sin (x - \frac{π}{4})

Simplificar

\frac{0.5}{2} : 0.35355 \dots

\frac{0.5}{2}

Convertir el elemento a una forma decimal

2 = 1.41421 \dots

= \frac{0.5}{1.41421 \dots}

Dividir:

\frac{0.5}{1.41421 \dots} = 0.35355 \dots

= 0.35355 \dots

sin (x - \frac{π}{4}) = 0.35355 \dots

sin (x - \frac{π}{4}) = 0.35355 \dots

sin (x - \frac{π}{4}) = 0.35355 \dots

Aplicar propiedades trigonométricas inversas

sin (x - \frac{π}{4}) = 0.35355 \dots

Soluciones generales para

sin (x - \frac{π}{4}) = 0.35355 \dots

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

x - \frac{π}{4} = arcsin (0.35355 \dots) + 2 πn, x - \frac{π}{4} = π - arcsin (0.35355 \dots) + 2 πn

x - \frac{π}{4} = arcsin (0.35355 \dots) + 2 πn, x - \frac{π}{4} = π - arcsin (0.35355 \dots) + 2 πn

Resolver

x - \frac{π}{4} = arcsin (0.35355 \dots) + 2 πn : x = arcsin (0.35355 \dots) + 2 πn + \frac{π}{4}

x - \frac{π}{4} = arcsin (0.35355 \dots) + 2 πn

Mover

\frac{π}{4}

al lado derecho

x - \frac{π}{4} = arcsin (0.35355 \dots) + 2 πn

Sumar

\frac{π}{4}

a ambos lados

x - \frac{π}{4} + \frac{π}{4} = arcsin (0.35355 \dots) + 2 πn + \frac{π}{4}

Simplificar

x = arcsin (0.35355 \dots) + 2 πn + \frac{π}{4}

x = arcsin (0.35355 \dots) + 2 πn + \frac{π}{4}

Resolver

x - \frac{π}{4} = π - arcsin (0.35355 \dots) + 2 πn : x = π - arcsin (0.35355 \dots) + 2 πn + \frac{π}{4}

x - \frac{π}{4} = π - arcsin (0.35355 \dots) + 2 πn

Mover

\frac{π}{4}

al lado derecho

x - \frac{π}{4} = π - arcsin (0.35355 \dots) + 2 πn

Sumar

\frac{π}{4}

a ambos lados

x - \frac{π}{4} + \frac{π}{4} = π - arcsin (0.35355 \dots) + 2 πn + \frac{π}{4}

Simplificar

x = π - arcsin (0.35355 \dots) + 2 πn + \frac{π}{4}

x = π - arcsin (0.35355 \dots) + 2 πn + \frac{π}{4}

x = arcsin (0.35355 \dots) + 2 πn + \frac{π}{4}, x = π - arcsin (0.35355 \dots) + 2 πn + \frac{π}{4}

Mostrar soluciones en forma decimal

x = 0.36136 \dots + 2 πn + \frac{π}{4}, x = π - 0.36136 \dots + 2 πn + \frac{π}{4}

Gráfica

Ejemplos populares

tan(t)= 1/4

tan (t) = \frac{1}{4}

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

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

solvefor y,tan(xy)=x resolver para

y, tan (x y) = x

cot^2(x)-3csc(x)+3=0

cot^{2} (x) - 3 csc (x) + 3 = 0

2sin^2(θ/2-pi/6)-1=0

2 sin^{2} (\frac{θ}{2} - \frac{π}{6}) - 1 = 0