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人気のある三角関数 >

sin^2(x)=((9m-9))/7

解

sin^{2} (x) = \frac{( 9 m - 9 )}{7}

解

x = arcsin (\frac{9 m - 9}{7}) + 2 πn, x = π + arcsin (- \frac{9 m - 9}{7}) + 2 πn, x = arcsin (- \frac{9 m - 9}{7}) + 2 πn, x = π + arcsin (\frac{9 m - 9}{7}) + 2 πn

解答ステップ

sin^{2} (x) = \frac{( 9 m - 9 )}{7}

置換で解く

sin^{2} (x) = \frac{9 m - 9}{7}

仮定:

sin (x) = u

u^{2} = \frac{9 m - 9}{7}

u^{2} = \frac{9 m - 9}{7} : u = \frac{9 m - 9}{7}, u = - \frac{9 m - 9}{7}

u^{2} = \frac{9 m - 9}{7}

x^{2} = f (a)

の場合, 解は

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

u = \frac{9 m - 9}{7}, u = - \frac{9 m - 9}{7}

代用を戻す

u = sin (x)

sin (x) = \frac{9 m - 9}{7}, sin (x) = - \frac{9 m - 9}{7}

sin (x) = \frac{9 m - 9}{7}, sin (x) = - \frac{9 m - 9}{7}

sin (x) = \frac{9 m - 9}{7} : x = arcsin (\frac{9 m - 9}{7}) + 2 πn, x = π + arcsin (- \frac{9 m - 9}{7}) + 2 πn

sin (x) = \frac{9 m - 9}{7}

三角関数の逆数プロパティを適用する

sin (x) = \frac{9 m - 9}{7}

以下の一般解

sin (x) = \frac{9 m - 9}{7}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (\frac{9 m - 9}{7}) + 2 πn, x = π + arcsin (- \frac{9 m - 9}{7}) + 2 πn

x = arcsin (\frac{9 m - 9}{7}) + 2 πn, x = π + arcsin (- \frac{9 m - 9}{7}) + 2 πn

sin (x) = - \frac{9 m - 9}{7} : x = arcsin (- \frac{9 m - 9}{7}) + 2 πn, x = π + arcsin (\frac{9 m - 9}{7}) + 2 πn

sin (x) = - \frac{9 m - 9}{7}

三角関数の逆数プロパティを適用する

sin (x) = - \frac{9 m - 9}{7}

以下の一般解

sin (x) = - \frac{9 m - 9}{7}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- \frac{9 m - 9}{7}) + 2 πn, x = π + arcsin (\frac{9 m - 9}{7}) + 2 πn

x = arcsin (- \frac{9 m - 9}{7}) + 2 πn, x = π + arcsin (\frac{9 m - 9}{7}) + 2 πn

すべての解を組み合わせる

x = arcsin (\frac{9 m - 9}{7}) + 2 πn, x = π + arcsin (- \frac{9 m - 9}{7}) + 2 πn, x = arcsin (- \frac{9 m - 9}{7}) + 2 πn, x = π + arcsin (\frac{9 m - 9}{7}) + 2 πn

グラフ

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