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人気のある >

81cos^2(x)=16

解

81 cos^{2} (x) = 16

解

x = 1.11024 \dots + 2 πn, x = 2 π - 1.11024 \dots + 2 πn, x = 2.03135 \dots + 2 πn, x = - 2.03135 \dots + 2 πn

+1

度

x = 63.61220 \dots^{\circ} + 36 0^{\circ} n, x = 296.38779 \dots^{\circ} + 36 0^{\circ} n, x = 116.38779 \dots^{\circ} + 36 0^{\circ} n, x = - 116.38779 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

81 cos^{2} (x) = 16

置換で解く

81 cos^{2} (x) = 16

仮定:

cos (x) = u

81 u^{2} = 16

81 u^{2} = 16 : u = \frac{4}{9}, u = - \frac{4}{9}

81 u^{2} = 16

以下で両辺を割る

81

81 u^{2} = 16

以下で両辺を割る

81

\frac{81 u ^{2}}{81} = \frac{16}{81}

簡素化

u^{2} = \frac{16}{81}

u^{2} = \frac{16}{81}

x^{2} = f (a)

の場合, 解は

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

u = \frac{16}{81}, u = - \frac{16}{81}

\frac{16}{81} = \frac{4}{9}

\frac{16}{81}

累乗根の規則を適用する:

, 以下を想定

a \geq 0, b \geq 0

= \frac{16}{81}

81 = 9

81

数を因数に分解する:

81 = 9^{2}

= 9^{2}

累乗根の規則を適用する:

9^{2} = 9

= 9

= \frac{16}{9}

16 = 4

16

数を因数に分解する:

16 = 4^{2}

= 4^{2}

累乗根の規則を適用する:

4^{2} = 4

= 4

= \frac{4}{9}

- \frac{16}{81} = - \frac{4}{9}

- \frac{16}{81}

簡素化

\frac{16}{81} : \frac{4}{9}

\frac{16}{81}

累乗根の規則を適用する:

, 以下を想定

a \geq 0, b \geq 0

= \frac{16}{81}

81 = 9

81

数を因数に分解する:

81 = 9^{2}

= 9^{2}

累乗根の規則を適用する:

9^{2} = 9

= 9

= \frac{16}{9}

16 = 4

16

数を因数に分解する:

16 = 4^{2}

= 4^{2}

累乗根の規則を適用する:

4^{2} = 4

= 4

= \frac{4}{9}

= - \frac{4}{9}

u = \frac{4}{9}, u = - \frac{4}{9}

代用を戻す

u = cos (x)

cos (x) = \frac{4}{9}, cos (x) = - \frac{4}{9}

cos (x) = \frac{4}{9}, cos (x) = - \frac{4}{9}

cos (x) = \frac{4}{9} : x = arccos (\frac{4}{9}) + 2 πn, x = 2 π - arccos (\frac{4}{9}) + 2 πn

cos (x) = \frac{4}{9}

三角関数の逆数プロパティを適用する

cos (x) = \frac{4}{9}

以下の一般解

cos (x) = \frac{4}{9}

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

x = arccos (\frac{4}{9}) + 2 πn, x = 2 π - arccos (\frac{4}{9}) + 2 πn

x = arccos (\frac{4}{9}) + 2 πn, x = 2 π - arccos (\frac{4}{9}) + 2 πn

cos (x) = - \frac{4}{9} : x = arccos (- \frac{4}{9}) + 2 πn, x = - arccos (- \frac{4}{9}) + 2 πn

cos (x) = - \frac{4}{9}

三角関数の逆数プロパティを適用する

cos (x) = - \frac{4}{9}

以下の一般解

cos (x) = - \frac{4}{9}

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

x = arccos (- \frac{4}{9}) + 2 πn, x = - arccos (- \frac{4}{9}) + 2 πn

x = arccos (- \frac{4}{9}) + 2 πn, x = - arccos (- \frac{4}{9}) + 2 πn

すべての解を組み合わせる

x = arccos (\frac{4}{9}) + 2 πn, x = 2 π - arccos (\frac{4}{9}) + 2 πn, x = arccos (- \frac{4}{9}) + 2 πn, x = - arccos (- \frac{4}{9}) + 2 πn

10進法形式で解を証明する

x = 1.11024 \dots + 2 πn, x = 2 π - 1.11024 \dots + 2 πn, x = 2.03135 \dots + 2 πn, x = - 2.03135 \dots + 2 πn

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