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

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

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cot(-(11pi)/3)

cot (- \frac{11 π}{3})

\frac{3}{3}

Decimal Notation

0.57735 \dots

Solution steps

cot (- \frac{11 π}{3})

Use the following property:

cot (- x) = - cot (x)

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

= - 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})

Simplify

= \frac{3}{3}

sin (2 \frac{π}{6})

sin (arcsin (- \frac{1}{53}))

arctan (\frac{22}{30})

arctan (sin (π))

2 π + sin (2 π)

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