sin(x)=(150)/(212.6)(sin(115))

解

sin (x) = \frac{150}{212.6} (sin (11 5^{\circ}))

x = 0.69377 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.69377 \dots + 36 0^{\circ} n

ラジアン

x = 0.69377 \dots + 2 πn, x = π - 0.69377 \dots + 2 πn

解答ステップ

sin (x) = \frac{150}{212.6} (sin (11 5^{\circ}))

三角関数の逆数プロパティを適用する

sin (x) = \frac{150}{212.6} sin (11 5^{\circ})

以下の一般解

sin (x) = \frac{150}{212.6} sin (11 5^{\circ})

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

x = arcsin (\frac{150}{212.6} sin (11 5^{\circ})) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{150}{212.6} sin (11 5^{\circ})) + 36 0^{\circ} n

x = arcsin (\frac{150}{212.6} sin (11 5^{\circ})) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{150}{212.6} sin (11 5^{\circ})) + 36 0^{\circ} n

10進法形式で解を証明する

x = 0.69377 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.69377 \dots + 36 0^{\circ} n