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

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

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tan((3pi)/5)

tan (\frac{3 π}{5})

- 5 + 25

Solution steps

tan (\frac{3 π}{5})

Rewrite using trig identities:

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

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

Rewrite using trig identities:

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

Rewrite using trig identities:

cos (\frac{3 π}{5}) = - \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

20 \cdot sin (6 0^{\circ})

cot (3 6^{\circ})

300 cos (3 0^{\circ})

sec (\frac{π}{3}) tan (\frac{π}{3})

csc (arctan (- 2))

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