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人気のある三角関数 >

cos^2(x)= 3/5

解

cos^{2} (x) = \frac{3}{5}

解

x = 0.68471 \dots + 2 πn, x = 2 π - 0.68471 \dots + 2 πn, x = 2.45687 \dots + 2 πn, x = - 2.45687 \dots + 2 πn

+1

度

x = 39.23152 \dots^{\circ} + 36 0^{\circ} n, x = 320.76847 \dots^{\circ} + 36 0^{\circ} n, x = 140.76847 \dots^{\circ} + 36 0^{\circ} n, x = - 140.76847 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

cos^{2} (x) = \frac{3}{5}

置換で解く

cos^{2} (x) = \frac{3}{5}

仮定:

cos (x) = u

u^{2} = \frac{3}{5}

u^{2} = \frac{3}{5} : u = \frac{3}{5}, u = - \frac{3}{5}

u^{2} = \frac{3}{5}

x^{2} = f (a)

の場合, 解は

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

u = \frac{3}{5}, u = - \frac{3}{5}

代用を戻す

u = cos (x)

cos (x) = \frac{3}{5}, cos (x) = - \frac{3}{5}

cos (x) = \frac{3}{5}, cos (x) = - \frac{3}{5}

cos (x) = \frac{3}{5} : x = arccos (\frac{3}{5}) + 2 πn, x = 2 π - arccos (\frac{3}{5}) + 2 πn

cos (x) = \frac{3}{5}

三角関数の逆数プロパティを適用する

cos (x) = \frac{3}{5}

以下の一般解

cos (x) = \frac{3}{5}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

x = arccos (\frac{3}{5}) + 2 πn, x = 2 π - arccos (\frac{3}{5}) + 2 πn

x = arccos (\frac{3}{5}) + 2 πn, x = 2 π - arccos (\frac{3}{5}) + 2 πn

cos (x) = - \frac{3}{5} : x = arccos (- \frac{3}{5}) + 2 πn, x = - arccos (- \frac{3}{5}) + 2 πn

cos (x) = - \frac{3}{5}

三角関数の逆数プロパティを適用する

cos (x) = - \frac{3}{5}

以下の一般解

cos (x) = - \frac{3}{5}

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

x = arccos (- \frac{3}{5}) + 2 πn, x = - arccos (- \frac{3}{5}) + 2 πn

x = arccos (- \frac{3}{5}) + 2 πn, x = - arccos (- \frac{3}{5}) + 2 πn

すべての解を組み合わせる

x = arccos (\frac{3}{5}) + 2 πn, x = 2 π - arccos (\frac{3}{5}) + 2 πn, x = arccos (- \frac{3}{5}) + 2 πn, x = - arccos (- \frac{3}{5}) + 2 πn

10進法形式で解を証明する

x = 0.68471 \dots + 2 πn, x = 2 π - 0.68471 \dots + 2 πn, x = 2.45687 \dots + 2 πn, x = - 2.45687 \dots + 2 πn

グラフ

人気の例

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1 - sec^{2} (x) = tan^{2} (x)

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