sec((9pi)/4)

解

sec (\frac{9 π}{4})

2

十進法表記

1.41421 \dots

解答ステップ

sec (\frac{9 π}{4})

sec (\frac{9 π}{4}) = sec (\frac{π}{4})

sec (\frac{9 π}{4})

\frac{9 π}{4}

を書き換え

2 π + \frac{π}{4}

= sec (2 π + \frac{π}{4})

以下の周期性を適用する:

sec

sec (x + 2 π) = sec (x)

sec (2 π + \frac{π}{4}) = sec (\frac{π}{4})

= sec (\frac{π}{4})

= sec (\frac{π}{4})

次の自明恒等式を使用する:

sec (\frac{π}{4}) = 2

sec (\frac{π}{4})

sec (x)

2 πn

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}

= 2

= 2