sin(x)=(123sin(70))/(184.5)

解

sin (x) = \frac{123 sin ( 7 0 ^{\circ} )}{184.5}

x = 0.67700 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.67700 \dots + 36 0^{\circ} n

ラジアン

x = 0.67700 \dots + 2 πn, x = π - 0.67700 \dots + 2 πn

解答ステップ

sin (x) = \frac{123 sin ( 7 0 ^{\circ} )}{184.5}

三角関数の逆数プロパティを適用する

sin (x) = \frac{123 sin ( 7 0 ^{\circ} )}{184.5}

以下の一般解

sin (x) = \frac{123 sin ( 7 0 ^{\circ} )}{184.5}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x = arcsin (\frac{123 sin ( 7 0 ^{\circ} )}{184.5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{123 sin ( 7 0 ^{\circ} )}{184.5}) + 36 0^{\circ} n

x = arcsin (\frac{123 sin ( 7 0 ^{\circ} )}{184.5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{123 sin ( 7 0 ^{\circ} )}{184.5}) + 36 0^{\circ} n

10進法形式で解を証明する

x = 0.67700 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.67700 \dots + 36 0^{\circ} n