What is the value of cot((9pi)/(10)) ?

The value of cot((9pi)/(10)) is -sqrt(5+2\sqrt{5)}

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cot((9pi)/(10))

cot (\frac{9 π}{10})

- 5 + 25

Solution steps

cot (\frac{9 π}{10})

Rewrite using trig identities:

\frac{cos ( \frac{9 π}{10} )}{sin ( \frac{9 π}{10} )}

= \frac{cos ( \frac{9 π}{10} )}{sin ( \frac{9 π}{10} )}

Rewrite using trig identities:

cos (\frac{9 π}{10}) = - \frac{2 5 + 5}{4}

Rewrite using trig identities:

sin (\frac{9 π}{10}) = \frac{2 3 - 5}{4}

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

Simplify

\frac{- \frac{2 5 + 5}{4}}{\frac{2 3 - 5}{4}} : - 5 + 25

= - 5 + 25

cot (\frac{3}{4})

csc (63 0^{\circ})

cos (arcsin (\frac{15}{17}))

arcsin (\frac{11}{12})

arctan (- \frac{1}{6})

What is the value of cot((9pi)/(10)) ?
The value of cot((9pi)/(10)) is -sqrt(5+2\sqrt{5)}