What is the value of sec(-840) ?

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sec(-840)

sec (- 84 0^{\circ})

- 2

Solution steps

sec (- 84 0^{\circ})

Use the following property:

sec (- x) = sec (x)

sec (- 84 0^{\circ}) = sec (84 0^{\circ})

= sec (84 0^{\circ})

sec (84 0^{\circ}) = sec (12 0^{\circ})

sec (84 0^{\circ})

Rewrite

84 0^{\circ}

36 0^{\circ} \cdot 2 + 12 0^{\circ}

= sec (36 0^{\circ} 2 + 12 0^{\circ})

Apply the periodicity of

sec

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

sec (36 0^{\circ} \cdot 2 + 12 0^{\circ}) = sec (12 0^{\circ})

= sec (12 0^{\circ})

= sec (12 0^{\circ})

Use the following trivial identity:

sec (12 0^{\circ}) = - 2

sec (12 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}

= - 2

= - 2

sec (arccos (- \frac{3}{5}))

sin (3 3^{\circ} + 4 2^{\circ})

6 sin (1 0^{\circ})

(cos (\frac{π}{4}) + i sin (\frac{π}{4}))^{100}

sin (6 \frac{π}{9})