What is the value of tan(1140) ?

The value of tan(1140) is square root of 3

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tan(1140)

tan (114 0^{\circ})

3

Decimal Notation

1.73205 \dots

Solution steps

tan (114 0^{\circ})

tan (114 0^{\circ}) = tan (6 0^{\circ})

tan (114 0^{\circ})

Rewrite

114 0^{\circ}

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

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

Apply the periodicity of

tan

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

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

= tan (6 0^{\circ})

= tan (6 0^{\circ})

Use the following trivial identity:

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

tan (6 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}

= 3

= 3

9.81 \cdot sin (2 5^{\circ})

arctan (\frac{20}{100})

sec (0.4)

sin (2 (3 5^{\circ}))

sin (1.047)