en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cot(θ)>0\land cos(θ)>0

Solution

cot (θ) > 0 and cos (θ) > 0

Solution

πn < θ < \frac{π}{2} + πn

+2

Interval Notation

(πn, \frac{π}{2} + πn)

Decimal Notation

πn < θ < 1.57079 \dots + πn

Solution steps

cot (θ) > 0 and cos (θ) > 0

cot (θ) > 0 : πn < θ < \frac{π}{2} + πn

cot (θ) > 0

If

cot (x) > a

then

πn < x < arccot (a) + πn

πn < θ < arccot (0) + πn

Simplify

arccot (0) : \frac{π}{2}

arccot (0)

Use the following trivial identity:

arccot (0) = \frac{π}{2}

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}{2}

πn < θ < \frac{π}{2} + πn

cos (θ) > 0 : - \frac{π}{2} + 2 πn < θ < \frac{π}{2} + 2 πn

cos (θ) > 0

For

cos (x) > a

, if

- 1 \leq a < 1

then

- arccos (a) + 2 πn < x < arccos (a) + 2 πn

- arccos (0) + 2 πn < θ < arccos (0) + 2 πn

Simplify

- arccos (0) : - \frac{π}{2}

- arccos (0)

Use the following trivial identity:

arccos (0) = \frac{π}{2}

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}

= - \frac{π}{2}

Simplify

arccos (0) : \frac{π}{2}

arccos (0)

Use the following trivial identity:

arccos (0) = \frac{π}{2}

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}

= \frac{π}{2}

- \frac{π}{2} + 2 πn < θ < \frac{π}{2} + 2 πn

Combine the intervals

πn < θ < \frac{π}{2} + πn and - \frac{π}{2} + 2 πn < θ < \frac{π}{2} + 2 πn

Merge Overlapping Intervals

πn < θ < \frac{π}{2} + πn

Popular Examples

sin(t)=-7/8 \land sec(t)<0

sin (t) = - \frac{7}{8} and sec (t) < 0

csc(θ)>0\land sec(θ)<0

csc (θ) > 0 and sec (θ) < 0

tan(θ)<0\land cos(θ)>0

tan (θ) < 0 and cos (θ) > 0

sec(θ)= 4/3 \land cot(θ)<0

sec (θ) = \frac{4}{3} and cot (θ) < 0

0<cos(x)<sin(x)

0 < cos (x) < sin (x)