What is the value of tan(210) ?

The value of tan(210) is (sqrt(3))/3

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tan(210)

tan (21 0^{\circ})

\frac{3}{3}

Decimal Notation

0.57735 \dots

Solution steps

tan (21 0^{\circ})

tan (21 0^{\circ}) = tan (3 0^{\circ})

tan (21 0^{\circ})

Rewrite

21 0^{\circ}

18 0^{\circ} + 3 0^{\circ}

= tan (18 0^{\circ} + 3 0^{\circ})

Apply the periodicity of

tan

tan (x + 18 0^{\circ}) = tan (x)

tan (18 0^{\circ} + 3 0^{\circ}) = tan (3 0^{\circ})

= tan (3 0^{\circ})

= tan (3 0^{\circ})

Use the following trivial identity:

tan (3 0^{\circ}) = \frac{3}{3}

tan (3 0^{\circ})

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= \frac{3}{3}

= \frac{3}{3}

2 tan (θ) - sec^{2} (θ) = 0

arcsinh (1)

tan (\frac{π}{4})

sin^{2} (x) = \frac{1}{4}, 0 \leq x \leq 2 π

tan (\frac{7 π}{6})