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

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

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cot((3pi)/5)

cot (\frac{3 π}{5})

- \frac{5 - 2 5}{5}

Solution steps

cot (\frac{3 π}{5})

Rewrite using trig identities:

\frac{cos ( \frac{3 π}{5} )}{sin ( \frac{3 π}{5} )}

= \frac{cos ( \frac{3 π}{5} )}{sin ( \frac{3 π}{5} )}

Rewrite using trig identities:

cos (\frac{3 π}{5}) = - \frac{2 3 - 5}{4}

Rewrite using trig identities:

sin (\frac{3 π}{5}) = \frac{2 5 + 5}{4}

= \frac{- \frac{2 3 - 5}{4}}{\frac{2 5 + 5}{4}}

Simplify

\frac{- \frac{2 3 - 5}{4}}{\frac{2 5 + 5}{4}} : - \frac{5 - 2 5}{5}

= - \frac{5 - 2 5}{5}

arccos (\frac{12}{129 \cdot 29})

sin (\frac{π ^{2}}{4})

sin (76 5^{\circ})

2 sinh (ln (2))

arccos (\frac{3}{2} - 3)

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