What is the value of cot(-(13pi)/6) ?

The value of cot(-(13pi)/6) is -sqrt(3)

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cot(-(13pi)/6)

cot (- \frac{13 π}{6})

- 3

Decimal Notation

- 1.73205 \dots

Solution steps

cot (- \frac{13 π}{6})

Use the following property:

cot (- x) = - cot (x)

cot (- \frac{13 π}{6}) = - cot (\frac{13 π}{6})

= - cot (\frac{13 π}{6})

cot (\frac{13 π}{6}) = cot (\frac{π}{6})

cot (\frac{13 π}{6})

Rewrite

\frac{13 π}{6}

π \cdot 2 + \frac{π}{6}

= cot (π 2 + \frac{π}{6})

Apply the periodicity of

cot

cot (x + π \cdot k) = cot (x)

cot (π \cdot 2 + \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{4 π}{5})

4 sin (- \frac{π}{2})

tan (90 0^{\circ})

arcsin (\frac{4}{10})

tan^{2} (4 5^{\circ} - 1 5^{\circ})