What is the value of cot(-(6pi)/5) ?

The value of cot(-(6pi)/5) is -((3sqrt(10)+5sqrt(2))sqrt(5-\sqrt{5)})/(20)

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cot(-(6pi)/5)

cot (- \frac{6 π}{5})

- \frac{( 3 10 + 5 2 ) 5 - 5}{20}

Solution steps

cot (- \frac{6 π}{5})

Use the following property:

cot (- x) = - cot (x)

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

= - cot (\frac{6 π}{5})

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

= - cot (\frac{π}{5})

Rewrite using trig identities:

cot (\frac{π}{5}) = \frac{( 3 10 + 5 2 ) 5 - 5}{20}

= - \frac{( 3 10 + 5 2 ) 5 - 5}{20}

sin (\frac{π}{6}) cos (\frac{π}{2}) + cos (\frac{π}{6}) sin (\frac{π}{2})

sin (30.9 6^{\circ})

arcsin (\frac{( 2 )}{2})

\frac{sin ( 6 0 ^{\circ} )}{sin ( 3 0 ^{\circ} )}

tan (\frac{5}{6} π)

What is the value of cot(-(6pi)/5) ?
The value of cot(-(6pi)/5) is -((3sqrt(10)+5sqrt(2))sqrt(5-\sqrt{5)})/(20)