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人気のある三角関数 >

7cos^2(x)-2=0

解

7 cos^{2} (x) - 2 = 0

解

x = 1.00685 \dots + 2 πn, x = 2 π - 1.00685 \dots + 2 πn, x = 2.13473 \dots + 2 πn, x = - 2.13473 \dots + 2 πn

+1

度

x = 57.68846 \dots^{\circ} + 36 0^{\circ} n, x = 302.31153 \dots^{\circ} + 36 0^{\circ} n, x = 122.31153 \dots^{\circ} + 36 0^{\circ} n, x = - 122.31153 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

7 cos^{2} (x) - 2 = 0

置換で解く

7 cos^{2} (x) - 2 = 0

仮定:

cos (x) = u

7 u^{2} - 2 = 0

7 u^{2} - 2 = 0 : u = \frac{2}{7}, u = - \frac{2}{7}

7 u^{2} - 2 = 0

2

を右側に移動します

7 u^{2} - 2 = 0

両辺に

2

を足す

7 u^{2} - 2 + 2 = 0 + 2

簡素化

7 u^{2} = 2

7 u^{2} = 2

以下で両辺を割る

7

7 u^{2} = 2

以下で両辺を割る

7

\frac{7 u ^{2}}{7} = \frac{2}{7}

簡素化

u^{2} = \frac{2}{7}

u^{2} = \frac{2}{7}

x^{2} = f (a)

の場合, 解は

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

u = \frac{2}{7}, u = - \frac{2}{7}

代用を戻す

u = cos (x)

cos (x) = \frac{2}{7}, cos (x) = - \frac{2}{7}

cos (x) = \frac{2}{7}, cos (x) = - \frac{2}{7}

cos (x) = \frac{2}{7} : x = arccos (\frac{2}{7}) + 2 πn, x = 2 π - arccos (\frac{2}{7}) + 2 πn

cos (x) = \frac{2}{7}

三角関数の逆数プロパティを適用する

cos (x) = \frac{2}{7}

以下の一般解

cos (x) = \frac{2}{7}

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

x = arccos (\frac{2}{7}) + 2 πn, x = 2 π - arccos (\frac{2}{7}) + 2 πn

x = arccos (\frac{2}{7}) + 2 πn, x = 2 π - arccos (\frac{2}{7}) + 2 πn

cos (x) = - \frac{2}{7} : x = arccos (- \frac{2}{7}) + 2 πn, x = - arccos (- \frac{2}{7}) + 2 πn

cos (x) = - \frac{2}{7}

三角関数の逆数プロパティを適用する

cos (x) = - \frac{2}{7}

以下の一般解

cos (x) = - \frac{2}{7}

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

x = arccos (- \frac{2}{7}) + 2 πn, x = - arccos (- \frac{2}{7}) + 2 πn

x = arccos (- \frac{2}{7}) + 2 πn, x = - arccos (- \frac{2}{7}) + 2 πn

すべての解を組み合わせる

x = arccos (\frac{2}{7}) + 2 πn, x = 2 π - arccos (\frac{2}{7}) + 2 πn, x = arccos (- \frac{2}{7}) + 2 πn, x = - arccos (- \frac{2}{7}) + 2 πn

10進法形式で解を証明する

x = 1.00685 \dots + 2 πn, x = 2 π - 1.00685 \dots + 2 πn, x = 2.13473 \dots + 2 πn, x = - 2.13473 \dots + 2 πn

グラフ

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