What is the value of tan(-900) ?

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tan(-900)

tan (- 90 0^{\circ})

0

Solution steps

tan (- 90 0^{\circ})

Use the following property:

tan (- x) = - tan (x)

tan (- 90 0^{\circ}) = - tan (90 0^{\circ})

= - tan (90 0^{\circ})

tan (90 0^{\circ}) = tan (0)

tan (90 0^{\circ})

Rewrite

90 0^{\circ}

18 0^{\circ} \cdot 5 + 0

= tan (18 0^{\circ} 5 + 0)

Apply the periodicity of

tan

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

tan (18 0^{\circ} \cdot 5 + 0) = tan (0)

= tan (0)

= - tan (0)

Use the following trivial identity:

tan (0) = 0

tan (0)

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}

= 0

= - 0

Simplify

= 0

cos (- \frac{19 π}{6})

cos (π) - sin (π)

cos (4 5^{\circ}) cos (3 0^{\circ}) - sin (4 5^{\circ}) sin (3 0^{\circ})

arctan (- \frac{2}{5})

arctan (- \frac{2}{0})