What is the value of tan((8pi)/3) ?

The value of tan((8pi)/3) is -sqrt(3)

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tan((8pi)/3)

tan (\frac{8 π}{3})

- 3

Solution steps

tan (\frac{8 π}{3})

tan (\frac{8 π}{3}) = tan (\frac{2 π}{3})

= tan (\frac{2 π}{3})

Rewrite using trig identities:

\frac{sin ( \frac{2 π}{3} )}{cos ( \frac{2 π}{3} )}

= \frac{sin ( \frac{2 π}{3} )}{cos ( \frac{2 π}{3} )}

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

= \frac{\frac{3}{2}}{- \frac{1}{2}}

Simplify

\frac{\frac{3}{2}}{- \frac{1}{2}} : - 3

= - 3

sin (2 (\frac{π}{4}))

arctan (\frac{15}{8})

arcsin (\frac{3}{3})

tan^{2} (1)

sin (13 5^{\circ}) - cos (3 0^{\circ})