What is the value of (tan(4pi))/3 ?

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(tan(4pi))/3

\frac{tan ( 4 π )}{3}

0

Solution steps

\frac{tan ( 4 π )}{3}

Rewrite using trig identities:

tan (4 π) = 0

tan (4 π)

tan (4 π) = tan (0)

tan (4 π)

Rewrite

4 π

π \cdot 4 + 0

= tan (π 4 + 0)

Apply the periodicity of

tan

tan (x + π \cdot k) = tan (x)

tan (π \cdot 4 + 0) = tan (0)

= tan (0)

= tan (0)

Use the following trivial identity:

tan (0) = 0

tan (0)

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 0

= 0

= \frac{0}{3}

Simplify

= 0

arccos (\frac{12}{100 4})

30 sin (3 8^{\circ})

arctan (- \frac{4}{21}) + 18 0^{\circ}

arccsc (23)

55 - 3 cos (\frac{180 ( 30 - 30 )}{180})