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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan((5pi)/3)

tan (\frac{5 π}{3})

- 3

Solution steps

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

cos (\frac{19 π}{12})

cos (7 π)

cos (1 0^{\circ})

tan (2)

3 tan^{3} (x) = tan (x)