What is the value of 8/(tan(60)) ?

The value of 8/(tan(60)) is (8sqrt(3))/3

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8/(tan(60))

\frac{8}{tan ( 6 0 ^{\circ} )}

\frac{8 3}{3}

Decimal Notation

4.61880 \dots

Solution steps

\frac{8}{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{8}{3}

Simplify

\frac{8}{3} : \frac{8 3}{3}

\frac{8}{3}

Multiply by the conjugate

\frac{3}{3}

= \frac{8 3}{3 3}

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= \frac{8 3}{3}

= \frac{8 3}{3}

cot (arctan (\frac{3}{4}))

3 (cos (\frac{π}{2}) + i sin (\frac{π}{2}))

sin (arccos (- \frac{3}{4}))

3 tan (2 0^{\circ})

arctan (2.3)