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人気のある三角関数 >

sin^2(x)=0.2

解

sin^{2} (x) = 0.2

解

x = 0.46364 \dots + 2 πn, x = π - 0.46364 \dots + 2 πn, x = - 0.46364 \dots + 2 πn, x = π + 0.46364 \dots + 2 πn

+1

度

x = 26.56505 \dots^{\circ} + 36 0^{\circ} n, x = 153.43494 \dots^{\circ} + 36 0^{\circ} n, x = - 26.56505 \dots^{\circ} + 36 0^{\circ} n, x = 206.56505 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

sin^{2} (x) = 0.2

置換で解く

sin^{2} (x) = 0.2

仮定:

sin (x) = u

u^{2} = 0.2

u^{2} = 0.2 : u = 0.2, u = - 0.2

u^{2} = 0.2

x^{2} = f (a)

の場合, 解は

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

u = 0.2, u = - 0.2

代用を戻す

u = sin (x)

sin (x) = 0.2, sin (x) = - 0.2

sin (x) = 0.2, sin (x) = - 0.2

sin (x) = 0.2 : x = arcsin (0.2) + 2 πn, x = π - arcsin (0.2) + 2 πn

sin (x) = 0.2

三角関数の逆数プロパティを適用する

sin (x) = 0.2

以下の一般解

sin (x) = 0.2

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (0.2) + 2 πn, x = π - arcsin (0.2) + 2 πn

x = arcsin (0.2) + 2 πn, x = π - arcsin (0.2) + 2 πn

sin (x) = - 0.2 : x = arcsin (- 0.2) + 2 πn, x = π + arcsin (0.2) + 2 πn

sin (x) = - 0.2

三角関数の逆数プロパティを適用する

sin (x) = - 0.2

以下の一般解

sin (x) = - 0.2

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- 0.2) + 2 πn, x = π + arcsin (0.2) + 2 πn

x = arcsin (- 0.2) + 2 πn, x = π + arcsin (0.2) + 2 πn

すべての解を組み合わせる

x = arcsin (0.2) + 2 πn, x = π - arcsin (0.2) + 2 πn, x = arcsin (- 0.2) + 2 πn, x = π + arcsin (0.2) + 2 πn

10進法形式で解を証明する

x = 0.46364 \dots + 2 πn, x = π - 0.46364 \dots + 2 πn, x = - 0.46364 \dots + 2 πn, x = π + 0.46364 \dots + 2 πn

グラフ

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