What is the value of cot((10pi)/3) ?

The value of cot((10pi)/3) is (sqrt(3))/3

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cot((10pi)/3)

cot (\frac{10 π}{3})

\frac{3}{3}

Decimal Notation

0.57735 \dots

Solution steps

cot (\frac{10 π}{3})

cot (\frac{10 π}{3}) = cot (\frac{π}{3})

cot (\frac{10 π}{3})

Rewrite

\frac{10 π}{3}

π \cdot 3 + \frac{π}{3}

= cot (π 3 + \frac{π}{3})

Apply the periodicity of

cot

cot (x + π \cdot k) = cot (x)

cot (π \cdot 3 + \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}

tan (18 0^{\circ}) - 2 cos (18 0^{\circ}) + 3 csc (27 0^{\circ}) + sin (9 0^{\circ})

sin (20 5^{\circ})

\frac{7}{tan ( 3 0 ^{\circ} )}

sin (14 π)

cos (arctan (\frac{3}{2}))