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

The value of tan(5/3 pi) is -sqrt(3)

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tan(5/3 pi)

tan (\frac{5}{3} π)

- 3

Solution steps

tan (\frac{5}{3} π)

Simplify:

\frac{5}{3} π = \frac{5 π}{3}

= tan (\frac{5 π}{3})

tan (\frac{5 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

12 cos (4 0^{\circ})

arctan (\frac{3.9}{5.3})

arctan (\frac{21}{20})

tan (arcsin (\frac{3}{5}) + \frac{π}{6})

tan (\frac{π}{4} + \frac{π}{3})