cos(x)=(22.5)/(34)

解

cos (x) = \frac{22.5}{34}

x = 0.84762 \dots + 2 πn, x = 2 π - 0.84762 \dots + 2 πn

度

x = 48.56540 \dots^{\circ} + 36 0^{\circ} n, x = 311.43459 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

cos (x) = \frac{22.5}{34}

三角関数の逆数プロパティを適用する

cos (x) = \frac{22.5}{34}

以下の一般解

cos (x) = \frac{22.5}{34}

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

x = arccos (\frac{22.5}{34}) + 2 πn, x = 2 π - arccos (\frac{22.5}{34}) + 2 πn

x = arccos (\frac{22.5}{34}) + 2 πn, x = 2 π - arccos (\frac{22.5}{34}) + 2 πn

10進法形式で解を証明する

x = 0.84762 \dots + 2 πn, x = 2 π - 0.84762 \dots + 2 πn