What is the value of cot((11pi)/3) ?

The value of cot((11pi)/3) is -(sqrt(3))/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cot((11pi)/3)

cot (\frac{11 π}{3})

- \frac{3}{3}

Decimal Notation

- 0.57735 \dots

Solution steps

cot (\frac{11 π}{3})

cot (\frac{11 π}{3}) = cot (\frac{2 π}{3})

cot (\frac{11 π}{3})

Rewrite

\frac{11 π}{3}

π \cdot 3 + \frac{2 π}{3}

= cot (π 3 + \frac{2 π}{3})

Apply the periodicity of

cot

cot (x + π \cdot k) = cot (x)

cot (π \cdot 3 + \frac{2 π}{3}) = cot (\frac{2 π}{3})

= cot (\frac{2 π}{3})

= cot (\frac{2 π}{3})

Use the following trivial identity:

cot (\frac{2 π}{3}) = - \frac{3}{3}

cot (\frac{2 π}{3})

cot (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= - \frac{3}{3}

= - \frac{3}{3}

25 cos (4 0^{\circ})

10 cos (7 0^{\circ})

arccos (\frac{1}{2 \cdot 29})

cos (\frac{π}{4} - \frac{π}{6})

sin (67.3 8^{\circ})