What is the value of 9/(sin(60)) ?

The value of 9/(sin(60)) is 6sqrt(3)

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9/(sin(60))

\frac{9}{sin ( 6 0 ^{\circ} )}

63

Decimal Notation

10.39230 \dots

Solution steps

\frac{9}{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{9}{\frac{3}{2}}

Simplify

\frac{9}{\frac{3}{2}} : 63

\frac{9}{\frac{3}{2}}

Apply the fraction rule:

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

= \frac{9 \cdot 2}{3}

Multiply the numbers:

9 \cdot 2 = 18

= \frac{18}{3}

Factor

18 : 3^{2} \cdot 2

Factor

18 = 3^{2} \cdot 2

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

Cancel

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

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

Apply radical rule:

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

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

Apply exponent rule:

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

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

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

Subtract the numbers:

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

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

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

3^{\frac{3}{2}} = 33

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

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

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

Apply exponent rule:

x^{a + b} = x^{a} x^{b}

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

Refine

= 33

= 2 \cdot 33

Multiply the numbers:

2 \cdot 3 = 6

= 63

= 63

\frac{1}{4} arctan (0)

arctan (\frac{6.8}{16})

sinh (ln (8))

\frac{10}{tan ( 2 7 ^{\circ} )}

- 2 cos (\frac{7 π}{4})