What is the value of tan((35pi)/6) ?

The value of tan((35pi)/6) is -(sqrt(3))/3

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tan((35pi)/6)

tan (\frac{35 π}{6})

- \frac{3}{3}

Solution steps

tan (\frac{35 π}{6})

tan (\frac{35 π}{6}) = tan (\frac{5 π}{6})

= tan (\frac{5 π}{6})

Rewrite using trig identities:

\frac{sin ( \frac{5 π}{6} )}{cos ( \frac{5 π}{6} )}

= \frac{sin ( \frac{5 π}{6} )}{cos ( \frac{5 π}{6} )}

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

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

Simplify

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

= - \frac{3}{3}

1 + cos^{2} (2)

150 sin (1 5^{\circ})

sin (- 0.001)

sin^{2} (7 8^{\circ}) + 1

cos (\frac{5}{3})