What is the value of 6/(tan(60)) ?

The value of 6/(tan(60)) is 2sqrt(3)

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6/(tan(60))

\frac{6}{tan ( 6 0 ^{\circ} )}

23

Decimal Notation

3.46410 \dots

Solution steps

\frac{6}{tan ( 6 0 ^{\circ} )}

Use the following trivial identity:

tan (6 0^{\circ}) = 3

tan (6 0^{\circ})

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 3

= \frac{6}{3}

Simplify

\frac{6}{3} : 23

\frac{6}{3}

Factor

6 : 2 \cdot 3

Factor

6 = 2 \cdot 3

= \frac{2 \cdot 3}{3}

Cancel

\frac{2 \cdot 3}{3} : 23

\frac{2 \cdot 3}{3}

Apply radical rule:

3 = 3^{\frac{1}{2}}

= \frac{2 \cdot 3}{3 ^{\frac{1}{2}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{3 ^{1}}{3 ^{\frac{1}{2}}} = 3^{1 - \frac{1}{2}}

= 2 \cdot 3^{- \frac{1}{2} + 1}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= 2 \cdot 3^{\frac{1}{2}}

Apply radical rule:

3^{\frac{1}{2}} = 3

= 23

= 23

= 23

π - arcsin (\frac{1}{3})

arcsin (- 0.1)

arctan (- 10)

500 sin (6 0^{\circ})

arccos (- \frac{2}{7})