What is the value of cot(-(5pi)/3) ?

The value of cot(-(5pi)/3) is (sqrt(3))/3

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cot(-(5pi)/3)

cot (- \frac{5 π}{3})

\frac{3}{3}

Decimal Notation

0.57735 \dots

Solution steps

cot (- \frac{5 π}{3})

Use the following property:

cot (- x) = - cot (x)

cot (- \frac{5 π}{3}) = - cot (\frac{5 π}{3})

= - cot (\frac{5 π}{3})

cot (\frac{5 π}{3}) = cot (\frac{2 π}{3})

cot (\frac{5 π}{3})

Rewrite

\frac{5 π}{3}

π + \frac{2 π}{3}

= cot (π + \frac{2 π}{3})

Apply the periodicity of

cot

cot (x + π) = cot (x)

cot (π + \frac{2 π}{3}) = cot (\frac{2 π}{3})

= cot (\frac{2 π}{3})

= - cot (\frac{2 π}{3})

Use the following trivial identity:

cot (\frac{2 π}{3}) = - \frac{3}{3}

cot (\frac{2 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})

Simplify

= \frac{3}{3}

arctan (\frac{6}{2})

sin (1 5^{\circ}) + sin (7 5^{\circ})

sin (25 0^{\circ})

arcsec (- 3)

4 sin (2 π)