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})

Use the following property:

sec (- x) = sec (x)

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

= 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}{sin ( 4 0 ^{\circ} )}

62 sin (\frac{7 π}{4})

arctan (\frac{5}{3})

sec (0.01)

2 + sin (\frac{3 π}{2})