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

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

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tan(-(4pi)/3)

tan (- \frac{4 π}{3})

- 3

Decimal Notation

- 1.73205 \dots

Solution steps

tan (- \frac{4 π}{3})

Use the following property:

tan (- x) = - tan (x)

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

2 sin^{2} (x) + 3 cos (x) - 3 = 0

sin (\frac{17 π}{12})

sin (x) = - 1

\frac{cos ( 3 x )}{cos ( x )} = 1 - 4 sin^{2} (x)

cos (- 2 π)