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

The value of 6/(sin(60)) is 4sqrt(3)

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6/(sin(60))

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

43

Decimal Notation

6.92820 \dots

Solution steps

\frac{6}{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{6}{\frac{3}{2}}

Simplify

\frac{6}{\frac{3}{2}} : 43

\frac{6}{\frac{3}{2}}

Apply the fraction rule:

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

= \frac{6 \cdot 2}{3}

Multiply the numbers:

6 \cdot 2 = 12

= \frac{12}{3}

Factor

12 : 2^{2} \cdot 3

Factor

12 = 2^{2} \cdot 3

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

Cancel

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

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

Apply radical rule:

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

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

Subtract the numbers:

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

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

Apply radical rule:

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

= 2^{2} 3

= 2^{2} 3

2^{2} = 4

= 43

= 43

cos (\frac{11 π}{2})

arccsc (- \frac{3}{2})

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

tan (arcsin (\frac{4}{5}) + arccos (1))

\frac{2 tan ( \frac{7 π}{8} )}{1 - tan ^{2} ( \frac{7 π}{8} )}