What is the value of tan((7pi)/3) ?

The value of tan((7pi)/3) is square root of 3

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tan((7pi)/3)

tan (\frac{7 π}{3})

3

Decimal Notation

1.73205 \dots

Solution steps

tan (\frac{7 π}{3})

tan (\frac{7 π}{3}) = tan (\frac{π}{3})

tan (\frac{7 π}{3})

Rewrite

\frac{7 π}{3}

π \cdot 2 + \frac{π}{3}

= tan (π 2 + \frac{π}{3})

Apply the periodicity of

tan

tan (x + π \cdot k) = tan (x)

tan (π \cdot 2 + \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

1 + tan (x) = 0

tan^{2} (x) - 3 = 0

cos (x) = \frac{3}{2}

cos (16 5^{\circ})

csc (2 π)

What is the value of tan((7pi)/3) ?
The value of tan((7pi)/3) is square root of 3