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Popular >

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

Solución

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

Solución

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = 0.72972 \dots + 2 πn, x = π - 0.72972 \dots + 2 πn

+1

Grados

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n, x = 41.81031 \dots^{\circ} + 36 0^{\circ} n, x = 138.18968 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

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

Factorizar

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

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

Factorizar el termino común

cos (x)

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

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

Resolver cada parte por separado

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

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

3 sin (x) - 2 = 0

Mover

2

al lado derecho

3 sin (x) - 2 = 0

Sumar

2

a ambos lados

3 sin (x) - 2 + 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 = 0.72972 \dots + 2 πn, x = π - 0.72972 \dots + 2 πn

Ejemplos populares

sin(x)=cos(x)+1

sin (x) = cos (x) + 1

5 sin (x) + 2 = 0

4 - sec^{2} (x) = 0

3 tan^{2} (x) - 9 = 0

3 cos (4 x) = 2