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

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

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cot((-11pi)/6)

cot (\frac{- 11 π}{6})

3

Decimal Notation

1.73205 \dots

Solution steps

cot (\frac{- 11 π}{6})

Simplify

= cot (- \frac{11 π}{6})

Use the following property:

cot (- x) = - cot (x)

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

= - 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)

Simplify

= 3

arccos (\frac{3}{18})

\frac{cos ( 0.01 ) - 1}{0.01}

cos (\frac{5 π}{18}) cos (\frac{2 π}{9}) - sin (\frac{5 π}{18}) sin (\frac{2 π}{9})

arcsin (sin (- \frac{7 π}{6}))

cos (9 8^{\circ})

What is the value of cot((-11pi)/6) ?
The value of cot((-11pi)/6) is square root of 3