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sin(x)tan(x-30)=0

Solución

sin (x) tan (x - 3 0^{\circ}) = 0

Solución

x = 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} n + 3 0^{\circ}

+1

radianes

x = 0 + 2 πn, x = π + 2 πn, x = \frac{π}{6} + πn

Pasos de solución

sin (x) tan (x - 3 0^{\circ}) = 0

Resolver cada parte por separado

sin (x) = 0 or tan (x - 3 0^{\circ}) = 0

sin (x) = 0 : x = 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

sin (x) = 0

Soluciones generales para

sin (x) = 0

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

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

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

Resolver

x = 0 + 36 0^{\circ} n : x = 36 0^{\circ} n

x = 0 + 36 0^{\circ} n

0 + 36 0^{\circ} n = 36 0^{\circ} n

x = 36 0^{\circ} n

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

tan (x - 3 0^{\circ}) = 0 : x = 18 0^{\circ} n + 3 0^{\circ}

tan (x - 3 0^{\circ}) = 0

Soluciones generales para

tan (x - 3 0^{\circ}) = 0

tan (x)

tabla de valores periódicos con

18 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x - 3 0^{\circ} = 0 + 18 0^{\circ} n

x - 3 0^{\circ} = 0 + 18 0^{\circ} n

Resolver

x - 3 0^{\circ} = 0 + 18 0^{\circ} n : x = 18 0^{\circ} n + 3 0^{\circ}

x - 3 0^{\circ} = 0 + 18 0^{\circ} n

0 + 18 0^{\circ} n = 18 0^{\circ} n

x - 3 0^{\circ} = 18 0^{\circ} n

Mover

3 0^{\circ}

al lado derecho

x - 3 0^{\circ} = 18 0^{\circ} n

Sumar

3 0^{\circ}

a ambos lados

x - 3 0^{\circ} + 3 0^{\circ} = 18 0^{\circ} n + 3 0^{\circ}

Simplificar

x = 18 0^{\circ} n + 3 0^{\circ}

x = 18 0^{\circ} n + 3 0^{\circ}

x = 18 0^{\circ} n + 3 0^{\circ}

Combinar toda las soluciones

x = 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} n + 3 0^{\circ}

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