What is the value of tan(-420) ?

The value of tan(-420) is -sqrt(3)

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tan(-420)

tan (- 42 0^{\circ})

- 3

Decimal Notation

- 1.73205 \dots

Solution steps

tan (- 42 0^{\circ})

Use the following property:

tan (- x) = - tan (x)

tan (- 42 0^{\circ}) = - tan (42 0^{\circ})

= - tan (42 0^{\circ})

tan (42 0^{\circ}) = tan (6 0^{\circ})

tan (42 0^{\circ})

Rewrite

42 0^{\circ}

18 0^{\circ} \cdot 2 + 6 0^{\circ}

= tan (18 0^{\circ} 2 + 6 0^{\circ})

Apply the periodicity of

tan

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

tan (18 0^{\circ} \cdot 2 + 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

6 sin (π)

2 cos (- 2)

sin (2 arcsin (\frac{4}{5}))

arcsin (- 0.75)

sin (4 5^{\circ}) \cdot 10