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Popular >

3cos(x)sin(x)=sin(x)

Solución

3 cos (x) sin (x) = sin (x)

Solución

x = 2 πn, x = π + 2 πn, x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn

+1

Grados

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 70.52877 \dots^{\circ} + 36 0^{\circ} n, x = 289.47122 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

3 cos (x) sin (x) = sin (x)

Restar

sin (x)

de ambos lados

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

Factorizar

3 cos (x) sin (x) - sin (x) : sin (x) (3 cos (x) - 1)

3 cos (x) sin (x) - sin (x)

Factorizar el termino común

sin (x)

= sin (x) (3 cos (x) - 1)

sin (x) (3 cos (x) - 1) = 0

Resolver cada parte por separado

sin (x) = 0 or 3 cos (x) - 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

Soluciones generales para

sin (x) = 0

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 = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

Resolver

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

3 cos (x) - 1 = 0 : x = arccos (\frac{1}{3}) + 2 πn, x = 2 π - arccos (\frac{1}{3}) + 2 πn

3 cos (x) - 1 = 0

Mover

1

al lado derecho

3 cos (x) - 1 = 0

Sumar

1

a ambos lados

3 cos (x) - 1 + 1 = 0 + 1

Simplificar

3 cos (x) = 1

3 cos (x) = 1

Dividir ambos lados entre

3

3 cos (x) = 1

Dividir ambos lados entre

3

\frac{3 cos ( x )}{3} = \frac{1}{3}

Simplificar

cos (x) = \frac{1}{3}

cos (x) = \frac{1}{3}

Aplicar propiedades trigonométricas inversas

cos (x) = \frac{1}{3}

Soluciones generales para

cos (x) = \frac{1}{3}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

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

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

Combinar toda las soluciones

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

Mostrar soluciones en forma decimal

x = 2 πn, x = π + 2 πn, x = 1.23095 \dots + 2 πn, x = 2 π - 1.23095 \dots + 2 πn

Ejemplos populares

2*sin(x)=sin(2x)

2 \cdot sin (x) = sin (2 x)

3sin(2((x-pi)/2))+1=2,5

3 sin (2 (\frac{x - π}{2})) + 1 = 2, 5

tan (x) = 0.4627

2sin^2(x)-4cos^2(x)+1=0

2 sin^{2} (x) - 4 cos^{2} (x) + 1 = 0

solvefor x,-y^2-cos(x)=0 resolver para

x, - y^{2} - cos (x) = 0