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cos(x-1)= 1/2 ,0<= x<= 360

Solución

cos (x - 1) = \frac{1}{2}, 0^{\circ} \leq x \leq 36 0^{\circ}

Solución

x = \frac{18 0 ^{\circ} + 3}{3}, x = \frac{90 0 ^{\circ} + 3}{3}

+1

radianes

x = \frac{π + 3}{3}, x = \frac{5 π + 3}{3}

Pasos de solución

cos (x - 1) = \frac{1}{2}, 0^{\circ} \leq x \leq 36 0^{\circ}

Soluciones generales para

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

cos (x)

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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x - 1 = 6 0^{\circ} + 36 0^{\circ} n, x - 1 = 30 0^{\circ} + 36 0^{\circ} n

x - 1 = 6 0^{\circ} + 36 0^{\circ} n, x - 1 = 30 0^{\circ} + 36 0^{\circ} n

Resolver

x - 1 = 6 0^{\circ} + 36 0^{\circ} n : x = 6 0^{\circ} + 36 0^{\circ} n + 1

x - 1 = 6 0^{\circ} + 36 0^{\circ} n

Mover

1

al lado derecho

x - 1 = 6 0^{\circ} + 36 0^{\circ} n

Sumar

1

a ambos lados

x - 1 + 1 = 6 0^{\circ} + 36 0^{\circ} n + 1

Simplificar

x = 6 0^{\circ} + 36 0^{\circ} n + 1

x = 6 0^{\circ} + 36 0^{\circ} n + 1

Resolver

x - 1 = 30 0^{\circ} + 36 0^{\circ} n : x = 30 0^{\circ} + 36 0^{\circ} n + 1

x - 1 = 30 0^{\circ} + 36 0^{\circ} n

Mover

1

al lado derecho

x - 1 = 30 0^{\circ} + 36 0^{\circ} n

Sumar

1

a ambos lados

x - 1 + 1 = 30 0^{\circ} + 36 0^{\circ} n + 1

Simplificar

x = 30 0^{\circ} + 36 0^{\circ} n + 1

x = 30 0^{\circ} + 36 0^{\circ} n + 1

x = 6 0^{\circ} + 36 0^{\circ} n + 1, x = 30 0^{\circ} + 36 0^{\circ} n + 1

Soluciones para el rango

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

x = \frac{18 0 ^{\circ} + 3}{3}, x = \frac{90 0 ^{\circ} + 3}{3}

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