What is the value of 4/(cos(30)) ?

The value of 4/(cos(30)) is (8sqrt(3))/3

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4/(cos(30))

\frac{4}{cos ( 3 0 ^{\circ} )}

\frac{8 3}{3}

Decimal Notation

4.61880 \dots

Solution steps

\frac{4}{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{4}{\frac{3}{2}}

Simplify

\frac{4}{\frac{3}{2}} : \frac{8 3}{3}

\frac{4}{\frac{3}{2}}

Apply the fraction rule:

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

= \frac{4 \cdot 2}{3}

Multiply the numbers:

4 \cdot 2 = 8

= \frac{8}{3}

Rationalize

\frac{8}{3} : \frac{8 3}{3}

\frac{8}{3}

Multiply by the conjugate

\frac{3}{3}

= \frac{8 3}{3 3}

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= \frac{8 3}{3}

= \frac{8 3}{3}

= \frac{8 3}{3}

arcsec (3) - arcsec (\frac{5}{3})

3 + 2 cos (\frac{π}{2})

sin (\frac{5}{13} - \frac{3}{5})

tan (arcsin (\frac{12}{25}) + arctan (\frac{12}{7}))

sin (arccos (\frac{8}{9}))