What is the value of 1/(sec(30)) ?

The value of 1/(sec(30)) is (sqrt(3))/2

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1/(sec(30))

\frac{1}{sec ( 3 0 ^{\circ} )}

\frac{3}{2}

Decimal Notation

0.86602 \dots

Solution steps

\frac{1}{sec ( 3 0 ^{\circ} )}

Use the following trivial identity:

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

sec (3 0^{\circ})

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= \frac{2 3}{3}

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

Simplify

\frac{1}{\frac{2 3}{3}} : \frac{3}{2}

\frac{1}{\frac{2 3}{3}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{3}{2 3}

Apply radical rule:

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

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

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

Subtract the numbers:

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

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

Apply radical rule:

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

= \frac{3}{2}

= \frac{3}{2}

arctan (\frac{4.99}{9.807} + 0.4)

cos (\frac{0.577}{53.2})

arcsec (\frac{2 2}{3})

sin (5 3^{\circ}) 50

2 cos (π + \frac{π}{4})