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Popular >

-1-cos(t)>= 0

Solución

- 1 - cos (t) \geq 0

Solución

t = π + 2 πn

+1

Notación decimal

t = 3.14159 \dots + 2 πn

Pasos de solución

- 1 - cos (t) \geq 0

Mover

1

al lado derecho

- 1 - cos (t) \geq 0

Sumar

1

a ambos lados

- 1 - cos (t) + 1 \geq 0 + 1

Simplificar

- cos (t) \geq 1

- cos (t) \geq 1

Multiplicar ambos lados por

- 1

- cos (t) \geq 1

Multiplicar ambos lados por -1 (invierte la desigualdad)

(- cos (t)) (- 1) \leq 1 \cdot (- 1)

Simplificar

cos (t) \leq - 1

cos (t) \leq - 1

Para

cos (x) \leq a

, si

- 1 < a < 1

entonces

arccos (a) + 2 πn \leq x \leq 2 π - arccos (a) + 2 πn

arccos (- 1) + 2 πn \leq t \leq 2 π - arccos (- 1) + 2 πn

Simplificar

arccos (- 1) : π

arccos (- 1)

Utilizar la siguiente identidad trivial:

arccos (- 1) = π

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= π

Simplificar

2 π - arccos (- 1) : π

2 π - arccos (- 1)

Utilizar la siguiente identidad trivial:

arccos (- 1) = π

x - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arccos (x) π \frac{5 π}{6} \frac{3 π}{4} \frac{2 π}{3} \frac{π}{2} \frac{π}{3} \frac{π}{4} \frac{π}{6} 0 arccos (x) 18 0^{\circ} 15 0^{\circ} 13 5^{\circ} 12 0^{\circ} 9 0^{\circ} 6 0^{\circ} 4 5^{\circ} 3 0^{\circ} 0^{\circ}

= 2 π - π

Sumar elementos similares:

2 π - π = π

= π

π + 2 πn \leq t \leq π + 2 πn

Simplificar

t = π + 2 πn

Ejemplos populares

cos (π x) < - \frac{1}{2}

cos (x) < 4

cos (x) < 5

sin(x)>= 0.5sqrt(3)

sin (x) \geq 0.5 3

cot(x)>(sqrt(3))/3

cot (x) > \frac{3}{3}