What is the value of cot((19pi)/6) ?

The value of cot((19pi)/6) is square root of 3

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cot((19pi)/6)

cot (\frac{19 π}{6})

3

Decimal Notation

1.73205 \dots

Solution steps

cot (\frac{19 π}{6})

cot (\frac{19 π}{6}) = cot (\frac{π}{6})

cot (\frac{19 π}{6})

Rewrite

\frac{19 π}{6}

π \cdot 3 + \frac{π}{6}

= cot (π 3 + \frac{π}{6})

Apply the periodicity of

cot

cot (x + π \cdot k) = cot (x)

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

= cot (\frac{π}{6})

= cot (\frac{π}{6})

Use the following trivial identity:

cot (\frac{π}{6}) = 3

cot (\frac{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

tan (\frac{- 5 π}{12})

sin (arctan (\frac{12}{5}))

arcsin (\frac{15}{17})

cos (arcsin (\frac{12}{13}))

sec (\frac{3 π}{4}) tan (\frac{3 π}{4})

What is the value of cot((19pi)/6) ?
The value of cot((19pi)/6) is square root of 3