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

The value of 8/(sin(60)) is (16sqrt(3))/3

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8/(sin(60))

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

\frac{16 3}{3}

Decimal Notation

9.23760 \dots

Solution steps

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

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 0^{\circ})

sin (x)

periodicity table with

36 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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{3}{2}

= \frac{8}{\frac{3}{2}}

Simplify

\frac{8}{\frac{3}{2}} : \frac{16 3}{3}

\frac{8}{\frac{3}{2}}

Apply the fraction rule:

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

= \frac{8 \cdot 2}{3}

Multiply the numbers:

8 \cdot 2 = 16

= \frac{16}{3}

Rationalize

\frac{16}{3} : \frac{16 3}{3}

\frac{16}{3}

Multiply by the conjugate

\frac{3}{3}

= \frac{16 3}{3 3}

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= \frac{16 3}{3}

= \frac{16 3}{3}

= \frac{16 3}{3}

\frac{tan ( 8 0 ^{\circ} ) + tan ( 4 0 ^{\circ} )}{1 - tan ( 8 0 ^{\circ} ) tan ( 4 0 ^{\circ} )}

2 cos (- 1)

\frac{tan ( 6 0 ^{\circ} ) - tan ( 3 0 ^{\circ} )}{1 + tan ( 6 0 ^{\circ} ) \cdot tan ( 3 0 ^{\circ} )}

arctan (1.333)

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