What is the value of (11)/(tan(30)) ?

The value of (11)/(tan(30)) is 11sqrt(3)

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(11)/(tan(30))

\frac{11}{tan ( 3 0 ^{\circ} )}

113

Decimal Notation

19.05255 \dots

Solution steps

\frac{11}{tan ( 3 0 ^{\circ} )}

Use the following trivial identity:

tan (3 0^{\circ}) = \frac{3}{3}

tan (3 0^{\circ})

tan (x)

periodicity table with

18 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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= \frac{3}{3}

= \frac{11}{\frac{3}{3}}

Simplify

\frac{11}{\frac{3}{3}} : 113

\frac{11}{\frac{3}{3}}

Apply the fraction rule:

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

= \frac{11 \cdot 3}{3}

Multiply the numbers:

11 \cdot 3 = 33

= \frac{33}{3}

Factor

33 : 3 \cdot 11

Factor

33 = 3 \cdot 11

= \frac{3 \cdot 11}{3}

Cancel

\frac{3 \cdot 11}{3} : 3 \cdot 11

\frac{3 \cdot 11}{3}

Apply radical rule:

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

= \frac{3 \cdot 11}{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}}

= 11 \cdot 3^{- \frac{1}{2} + 1}

Subtract the numbers:

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

= 11 \cdot 3^{\frac{1}{2}}

Apply radical rule:

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

= 113

= 3 \cdot 11

= 113

(sin (5 5^{\circ}))^{2}

sec^{2} (0 + 0)

sin^{2} (π) + cos^{2} (π)

\frac{1}{cos ^{2} ( \frac{π}{6} )}

\frac{16.58}{2} \cdot sin (4^{\circ})