sec(540)

解

sec (54 0^{\circ})

- 1

解答ステップ

sec (54 0^{\circ})

sec (54 0^{\circ}) = sec (18 0^{\circ})

sec (54 0^{\circ})

54 0^{\circ}

を書き換え

36 0^{\circ} + 18 0^{\circ}

= sec (36 0^{\circ} + 18 0^{\circ})

以下の周期性を適用する:

sec

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

sec (36 0^{\circ} + 18 0^{\circ}) = sec (18 0^{\circ})

= sec (18 0^{\circ})

= sec (18 0^{\circ})

次の自明恒等式を使用する:

sec (18 0^{\circ}) = (- 1)

sec (18 0^{\circ})

sec (x)

36 0^{\circ} n

循環を含む周期性テーブル :

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= (- 1)

= - 1