What is the value of cot((-19pi)/3) ?

The value of cot((-19pi)/3) is -(sqrt(3))/3

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cot((-19pi)/3)

cot (\frac{- 19 π}{3})

- \frac{3}{3}

Decimal

- 0.57735 \dots

Solution steps

cot (\frac{- 19 π}{3})

Simplify

= cot (- \frac{19 π}{3})

Use the following property:

cot (- x) = - cot (x)

cot (- \frac{19 π}{3}) = - cot (\frac{19 π}{3})

= - cot (\frac{19 π}{3})

cot (\frac{19 π}{3}) = cot (\frac{π}{3})

cot (\frac{19 π}{3})

Rewrite

\frac{19 π}{3}

π \cdot 6 + \frac{π}{3}

= cot (π 6 + \frac{π}{3})

Apply the periodicity of

cot

cot (x + π \cdot k) = cot (x)

cot (π \cdot 6 + \frac{π}{3}) = cot (\frac{π}{3})

= cot (\frac{π}{3})

= - cot (\frac{π}{3})

Use the following trivial identity:

cot (\frac{π}{3}) = \frac{3}{3}

cot (\frac{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}

What is the value of cot((-19pi)/3) ?
The value of cot((-19pi)/3) is -(sqrt(3))/3