What is the value of 3tan((7pi)/6) ?

The value of 3tan((7pi)/6) is square root of 3

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3tan((7pi)/6)

3 tan (\frac{7 π}{6})

3

Decimal Notation

1.73205 \dots

Solution steps

3 tan (\frac{7 π}{6})

Rewrite using trig identities:

tan (\frac{7 π}{6}) = \frac{3}{3}

tan (\frac{7 π}{6})

tan (\frac{7 π}{6}) = tan (\frac{π}{6})

tan (\frac{7 π}{6})

Rewrite

\frac{7 π}{6}

π + \frac{π}{6}

= tan (π + \frac{π}{6})

Apply the periodicity of

tan

tan (x + π) = tan (x)

tan (π + \frac{π}{6}) = tan (\frac{π}{6})

= tan (\frac{π}{6})

= tan (\frac{π}{6})

Use the following trivial identity:

tan (\frac{π}{6}) = \frac{3}{3}

tan (\frac{π}{6})

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}

= \frac{3}{3}

= \frac{3}{3}

= 3 \cdot \frac{3}{3}

Simplify

3 \cdot \frac{3}{3} : 3

3 \cdot \frac{3}{3}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 \cdot 3}{3}

Cancel the common factor:

3

= 3

= 3

- 3 sin (\frac{2 π}{3})

csc (\frac{13 π}{12})

sin (2 \cdot 3 5^{\circ})

\frac{tan ( 2 )}{tan ( 4 )}

sin (\frac{π}{2} 3)

What is the value of 3tan((7pi)/6) ?
The value of 3tan((7pi)/6) is square root of 3