en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cot^2(x)>= 1/3

Solution

cot^{2} (x) \geq \frac{1}{3}

Solution

πn < x \leq \frac{π}{3} + πn or \frac{2 π}{3} + πn \leq x < π + πn

+2

Interval Notation

(πn, \frac{π}{3} + πn] \cup [\frac{2 π}{3} + πn, π + πn)

Decimal Notation

πn < x \leq 1.04719 \dots + πn or 2.09439 \dots + πn \leq x < 3.14159 \dots + πn

Solution steps

cot^{2} (x) \geq \frac{1}{3}

For

u^{n} \geq a

, if

n

is even then

cot (x) \leq - \frac{1}{3} or cot (x) \geq \frac{1}{3}

cot (x) \leq - \frac{1}{3} : \frac{2 π}{3} + πn \leq x < π + πn

cot (x) \leq - \frac{1}{3}

If

cot (x) \leq a

then

arccot (a) + πn \leq x < π + πn

arccot (- \frac{1}{3}) + πn \leq x < π + πn

Simplify

arccot (- \frac{1}{3}) : \frac{2 π}{3}

arccot (- \frac{1}{3})

Use the following trivial identity:

arccot (- \frac{1}{3}) = \frac{2 π}{3}

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

= \frac{2 π}{3}

\frac{2 π}{3} + πn \leq x < π + πn

cot (x) \geq \frac{1}{3} : πn < x \leq \frac{π}{3} + πn

cot (x) \geq \frac{1}{3}

If

cot (x) \geq a

then

πn < x \leq arccot (a) + πn

πn < x \leq arccot (\frac{1}{3}) + πn

Simplify

arccot (\frac{1}{3}) : \frac{π}{3}

arccot (\frac{1}{3})

Use the following trivial identity:

arccot (\frac{1}{3}) = \frac{π}{3}

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

= \frac{π}{3}

πn < x \leq \frac{π}{3} + πn

Combine the intervals

\frac{2 π}{3} + πn \leq x < π + πn or πn < x \leq \frac{π}{3} + πn

Merge Overlapping Intervals

πn < x \leq \frac{π}{3} + πn or \frac{2 π}{3} + πn \leq x < π + πn

Popular Examples

2cos(x)>cos(2x)

2 cos (x) > cos (2 x)

tan^{2} (x) < 1

2sin^2(x)+3sin(x)+1>0

2 sin^{2} (x) + 3 sin (x) + 1 > 0

sin(2t)<1,(0,2pi)

sin (2 t) < 1, (0, 2 π)

2sin^2(x)-3sin(x)+1<= 0

2 sin^{2} (x) - 3 sin (x) + 1 \leq 0