What is the value of (12)/(cos(30)) ?

The value of (12)/(cos(30)) is 8sqrt(3)

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(12)/(cos(30))

\frac{12}{cos ( 3 0 ^{\circ} )}

83

Decimal Notation

13.85640 \dots

Solution steps

\frac{12}{cos ( 3 0 ^{\circ} )}

Use the following trivial identity:

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

cos (3 0^{\circ})

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

= \frac{12}{\frac{3}{2}}

Simplify

\frac{12}{\frac{3}{2}} : 83

\frac{12}{\frac{3}{2}}

Apply the fraction rule:

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

= \frac{12 \cdot 2}{3}

Multiply the numbers:

12 \cdot 2 = 24

= \frac{24}{3}

Factor

24 : 2^{3} \cdot 3

Factor

24 = 2^{3} \cdot 3

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

Cancel

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

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

Apply radical rule:

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

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

Subtract the numbers:

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

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

Apply radical rule:

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

= 2^{3} 3

= 2^{3} 3

2^{3} = 8

= 83

= 83

sin (\frac{- 8 π}{3})

arctan (0.98)

cos (\frac{1}{100})

cos (arctan (\frac{15}{8}) + arcsin (\frac{40}{41}))

arctan (0.54)