What is the value of tan(1110) ?

The value of tan(1110) is (sqrt(3))/3

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tan(1110)

tan (111 0^{\circ})

\frac{3}{3}

Decimal Notation

0.57735 \dots

Solution steps

tan (111 0^{\circ})

tan (111 0^{\circ}) = tan (3 0^{\circ})

tan (111 0^{\circ})

Rewrite

111 0^{\circ}

18 0^{\circ} \cdot 6 + 3 0^{\circ}

= tan (18 0^{\circ} 6 + 3 0^{\circ})

Apply the periodicity of

tan

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

tan (18 0^{\circ} \cdot 6 + 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}

arctan (\frac{50}{60})

3 sin (22 5^{\circ})

\frac{5.07}{sin ( 6 5 ^{\circ} )}

arctan (- \frac{2}{9})

80 \cdot cos (4 5^{\circ})