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sin(2x)sin(x)=0,0<= x<= 360

Solución

sin (2 x) sin (x) = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

x = 0, x = 9 0^{\circ}, x = 18 0^{\circ}, x = 27 0^{\circ}, x = 36 0^{\circ}

radianes

x = 0, x = \frac{π}{2}, x = π, x = \frac{3 π}{2}, x = 2 π

Pasos de solución

sin (2 x) sin (x) = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

Resolver cada parte por separado

sin (2 x) = 0 or sin (x) = 0

sin (2 x) = 0, 0 \leq x \leq 36 0^{\circ} : x = 0, x = 9 0^{\circ}, x = 18 0^{\circ}, x = 27 0^{\circ}, x = 36 0^{\circ}

sin (2 x) = 0, 0 \leq x \leq 36 0^{\circ}

Soluciones generales para

sin (2 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}

2 x = 0 + 36 0^{\circ} n, 2 x = 18 0^{\circ} + 36 0^{\circ} n

2 x = 0 + 36 0^{\circ} n, 2 x = 18 0^{\circ} + 36 0^{\circ} n

Resolver

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

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

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

2 x = 36 0^{\circ} n

Dividir ambos lados entre

2

2 x = 36 0^{\circ} n

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{36 0 ^{\circ} n}{2}

Simplificar

x = 18 0^{\circ} n

x = 18 0^{\circ} n

Resolver

2 x = 18 0^{\circ} + 36 0^{\circ} n : x = 9 0^{\circ} + 18 0^{\circ} n

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

Dividir ambos lados entre

2

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

Dividir ambos lados entre

2

\frac{2 x}{2} = 9 0^{\circ} + \frac{36 0 ^{\circ} n}{2}

Simplificar

x = 9 0^{\circ} + 18 0^{\circ} n

x = 9 0^{\circ} + 18 0^{\circ} n

x = 18 0^{\circ} n, x = 9 0^{\circ} + 18 0^{\circ} n

Soluciones para el rango

0 \leq x \leq 36 0^{\circ}

x = 0, x = 9 0^{\circ}, x = 18 0^{\circ}, x = 27 0^{\circ}, x = 36 0^{\circ}

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

sin (x) = 0, 0 \leq x \leq 36 0^{\circ}

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

Soluciones para el rango

0 \leq x \leq 36 0^{\circ}

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

Combinar toda las soluciones

x = 0, x = 9 0^{\circ}, x = 18 0^{\circ}, x = 27 0^{\circ}, x = 36 0^{\circ}

cot^{2} (x) = csc (x) + 1

cos (x) - sin (x) = 0.5

sin (x + π) - sin (x) + 3 = 0

csc (x) = 1.5

tan (t) = 0