cos(y_{0})=((a_{0}*n_{0}))/(\mid)a_{0}\mid

解

cos (y_{0}) = \frac{( a _{0} \cdot n _{0} )}{∣} a_{0} ∣

y_{0} = arccos (a_{0}^{2} n_{0}) + 2 πn, y_{0} = - arccos (a_{0}^{2} n_{0}) + 2 πn

解答ステップ

cos (y_{0}) = \frac{( a _{0} n _{0} )}{∣} a_{0} ∣

簡素化

\frac{a _{0} n _{0}}{∣} a_{0} ∣ : a_{0}^{2} n_{0}

\frac{a _{0} n _{0}}{∣} a_{0} ∣

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{a _{0} n _{0} a _{0} ∣}{∣}

共通因数を約分する:

∣

= a_{0} n_{0} a_{0}

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

a_{0} a_{0} = a_{0}^{1 + 1}

= n_{0} a_{0}^{1 + 1}

数を足す:

1 + 1 = 2

= n_{0} a_{0}^{2}

三角関数の逆数プロパティを適用する

cos (y_{0}) = a_{0}^{2} n_{0}

以下の一般解

cos (y_{0}) = a_{0}^{2} n_{0}

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

y_{0} = arccos (a_{0}^{2} n_{0}) + 2 πn, y_{0} = - arccos (a_{0}^{2} n_{0}) + 2 πn

y_{0} = arccos (a_{0}^{2} n_{0}) + 2 πn, y_{0} = - arccos (a_{0}^{2} n_{0}) + 2 πn