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人気のある三角関数 >

sec^2(x)=(3sqrt(3))/pi

解

sec^{2} (x) = \frac{3 3}{π}

解

x = 0.68001 \dots + 2 πn, x = 2 π - 0.68001 \dots + 2 πn, x = 2.46157 \dots + 2 πn, x = - 2.46157 \dots + 2 πn

+1

度

x = 38.96227 \dots^{\circ} + 36 0^{\circ} n, x = 321.03772 \dots^{\circ} + 36 0^{\circ} n, x = 141.03772 \dots^{\circ} + 36 0^{\circ} n, x = - 141.03772 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

sec^{2} (x) = \frac{3 3}{π}

置換で解く

sec^{2} (x) = \frac{3 3}{π}

仮定:

sec (x) = u

u^{2} = \frac{3 3}{π}

u^{2} = \frac{3 3}{π} : u = \frac{3 3}{π}, u = - \frac{3 3}{π}

u^{2} = \frac{3 3}{π}

x^{2} = f (a)

の場合, 解は

x = f (a), - f (a)

u = \frac{3 3}{π}, u = - \frac{3 3}{π}

代用を戻す

u = sec (x)

sec (x) = \frac{3 3}{π}, sec (x) = - \frac{3 3}{π}

sec (x) = \frac{3 3}{π}, sec (x) = - \frac{3 3}{π}

sec (x) = \frac{3 3}{π} : x = arcsec \frac{3 3}{π} + 2 πn, x = 2 π - arcsec \frac{3 3}{π} + 2 πn

sec (x) = \frac{3 3}{π}

三角関数の逆数プロパティを適用する

sec (x) = \frac{3 3}{π}

以下の一般解

sec (x) = \frac{3 3}{π}

sec (x) = a \Rightarrow x = arcsec (a) + 2 πn, x = 2 π - arcsec (a) + 2 πn

x = arcsec \frac{3 3}{π} + 2 πn, x = 2 π - arcsec \frac{3 3}{π} + 2 πn

x = arcsec \frac{3 3}{π} + 2 πn, x = 2 π - arcsec \frac{3 3}{π} + 2 πn

sec (x) = - \frac{3 3}{π} : x = arcsec - \frac{3 3}{π} + 2 πn, x = - arcsec - \frac{3 3}{π} + 2 πn

sec (x) = - \frac{3 3}{π}

三角関数の逆数プロパティを適用する

sec (x) = - \frac{3 3}{π}

以下の一般解

sec (x) = - \frac{3 3}{π}

sec (x) = - a \Rightarrow x = arcsec (- a) + 2 πn, x = - arcsec (- a) + 2 πn

x = arcsec - \frac{3 3}{π} + 2 πn, x = - arcsec - \frac{3 3}{π} + 2 πn

x = arcsec - \frac{3 3}{π} + 2 πn, x = - arcsec - \frac{3 3}{π} + 2 πn

すべての解を組み合わせる

x = arcsec \frac{3 3}{π} + 2 πn, x = 2 π - arcsec \frac{3 3}{π} + 2 πn, x = arcsec - \frac{3 3}{π} + 2 πn, x = - arcsec - \frac{3 3}{π} + 2 πn

10進法形式で解を証明する

x = 0.68001 \dots + 2 πn, x = 2 π - 0.68001 \dots + 2 πn, x = 2.46157 \dots + 2 πn, x = - 2.46157 \dots + 2 πn

グラフ

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