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

The value of tan((4pi)/3)-sqrt(3) is 0

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tan((4pi)/3)-sqrt(3)

tan (\frac{4 π}{3}) - 3

0

Solution steps

tan (\frac{4 π}{3}) - 3

Rewrite using trig identities:

tan (\frac{4 π}{3}) = 3

tan (\frac{4 π}{3})

tan (\frac{4 π}{3}) = tan (\frac{π}{3})

tan (\frac{4 π}{3})

Rewrite

\frac{4 π}{3}

π + \frac{π}{3}

= tan (π + \frac{π}{3})

Apply the periodicity of

tan

tan (x + π) = tan (x)

tan (π + \frac{π}{3}) = tan (\frac{π}{3})

= tan (\frac{π}{3})

= tan (\frac{π}{3})

Use the following trivial identity:

tan (\frac{π}{3}) = 3

tan (\frac{π}{3})

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}

= 3

= 3

= 3 - 3

Simplify

= 0

arctan (\frac{9.3}{7.5})

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

sin (arcsec (4))

csc^{2} (- 1)

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

What is the value of tan((4pi)/3)-sqrt(3) ?
The value of tan((4pi)/3)-sqrt(3) is 0