What is the value of cot((11pi)/6) ?

The value of cot((11pi)/6) is -sqrt(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cot((11pi)/6)

cot (\frac{11 π}{6})

- 3

Decimal Notation

- 1.73205 \dots

Solution steps

cot (\frac{11 π}{6})

cot (\frac{11 π}{6}) = cot (\frac{5 π}{6})

cot (\frac{11 π}{6})

Rewrite

\frac{11 π}{6}

π + \frac{5 π}{6}

= cot (π + \frac{5 π}{6})

Apply the periodicity of

cot

cot (x + π) = cot (x)

cot (π + \frac{5 π}{6}) = cot (\frac{5 π}{6})

= cot (\frac{5 π}{6})

= cot (\frac{5 π}{6})

Use the following trivial identity:

cot (\frac{5 π}{6}) = - 3

cot (\frac{5 π}{6})

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

= - 3

= - 3

sec (2 π)

arctan (\frac{1}{3})

3 tan^{2} (x) - 1 = 0

sin (θ) = 0

3 cot (θ) - 1 = 0