What is the value of 3/(sin(60)) ?

The value of 3/(sin(60)) is 2sqrt(3)

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3/(sin(60))

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

23

Decimal Notation

3.46410 \dots

Solution steps

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

Simplify

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

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

Apply the fraction rule:

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

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

Multiply the numbers:

3 \cdot 2 = 6

= \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

arctan (4.5)

cos^{2} (0) + sin^{2} (0)

2 (cos (3 0^{\circ}))^{2} + 3 (sin (3 0^{\circ}))^{2}

sin (73 5^{\circ})

\frac{cos ^{3} ( \frac{π}{2} )}{3}