What is the value of cot((4pi)/3) ?

The value of cot((4pi)/3) is (sqrt(3))/3

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cot((4pi)/3)

cot (\frac{4 π}{3})

\frac{3}{3}

Decimal Notation

0.57735 \dots

Solution steps

cot (\frac{4 π}{3})

cot (\frac{4 π}{3}) = cot (\frac{π}{3})

cot (\frac{4 π}{3})

Rewrite

\frac{4 π}{3}

π + \frac{π}{3}

= cot (π + \frac{π}{3})

Apply the periodicity of

cot

cot (x + π) = cot (x)

cot (π + \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}

cot (x) = 1, 0 \leq x \leq 2 π

sin^{2} (x) = \frac{1}{4}

tan (- \frac{π}{4})

3 tan (θ) + 1 = 0

sin (x) cos (y) = \frac{1}{2} (sin (x + y) + sin (x - y))