What is the value of sec(390) ?

The value of sec(390) is (2sqrt(3))/3

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sec(390)

sec (39 0^{\circ})

\frac{2 3}{3}

Decimal Notation

1.15470 \dots

Solution steps

sec (39 0^{\circ})

sec (39 0^{\circ}) = sec (3 0^{\circ})

sec (39 0^{\circ})

Rewrite

39 0^{\circ}

36 0^{\circ} + 3 0^{\circ}

= sec (36 0^{\circ} + 3 0^{\circ})

Apply the periodicity of

sec

sec (x + 36 0^{\circ}) = sec (x)

sec (36 0^{\circ} + 3 0^{\circ}) = sec (3 0^{\circ})

= sec (3 0^{\circ})

= 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{2 3}{3}

\frac{8 tan ( \frac{π}{8} )}{1 - tan ^{2} ( \frac{π}{8} )}

cos^{2} (8)

sin (arcsin (\frac{3}{5}) - arccos (- \frac{8}{17}))

cos (\frac{π}{2}) - \frac{π}{2} sin (\frac{π}{2})

1000 cos (3 0^{\circ})