What is the value of cot((23pi)/6) ?

The value of cot((23pi)/6) is -sqrt(3)

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cot((23pi)/6)

cot (\frac{23 π}{6})

- 3

Decimal Notation

- 1.73205 \dots

Solution steps

cot (\frac{23 π}{6})

cot (\frac{23 π}{6}) = cot (\frac{5 π}{6})

cot (\frac{23 π}{6})

Rewrite

\frac{23 π}{6}

π \cdot 3 + \frac{5 π}{6}

= cot (π 3 + \frac{5 π}{6})

Apply the periodicity of

cot

cot (x + π \cdot k) = cot (x)

cot (π \cdot 3 + \frac{5 π}{6}) = cot (\frac{5 π}{6})

= cot (\frac{5 π}{6})

= cot (\frac{5 π}{6})

Use the following trivial identity:

cot (\frac{5 π}{6}) = - 3

cot (\frac{5 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

arccos (6)

\frac{1 - cos ( 3 0 ^{\circ} )}{2}

arcsin (- \frac{1}{5})

1 - 2 sin^{2} (10 5^{\circ})

arcsin (sin (\frac{7 π}{8}))