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Popular Trigonometry >

-1-cos(t)>= 0

Solution

- 1 - cos (t) \geq 0

Solution

t = π + 2 πn

+1

Decimal

t = 3.14159 \dots + 2 πn

Solution steps

- 1 - cos (t) \geq 0

Move

1

to the right side

- 1 - cos (t) \geq 0

Add

1

to both sides

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

Simplify

- cos (t) \geq 1

- cos (t) \geq 1

Multiply both sides by

- 1

- cos (t) \geq 1

Multiply both sides by -1 (reverse the inequality)

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

Simplify

cos (t) \leq - 1

cos (t) \leq - 1

For

cos (x) \leq a

, if

- 1 < a < 1

then

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

Simplify

arccos (- 1) : π

arccos (- 1)

Use the following trivial identity:

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

Simplify

2 π - arccos (- 1) : π

2 π - arccos (- 1)

Use the following trivial identity:

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

Add similar elements:

2 π - π = π

= π

π + 2 πn \leq t \leq π + 2 πn

Simplify

t = π + 2 πn

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