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人気のある三角関数 >

sin^{22}(x)=0.5

解

sin^{22} (x) = 0.5

解

x = 1.32108 \dots + 2 πn, x = π - 1.32108 \dots + 2 πn, x = - 1.32108 \dots + 2 πn, x = π + 1.32108 \dots + 2 πn

+1

度

x = 75.69275 \dots^{\circ} + 36 0^{\circ} n, x = 104.30724 \dots^{\circ} + 36 0^{\circ} n, x = - 75.69275 \dots^{\circ} + 36 0^{\circ} n, x = 255.69275 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

sin^{22} (x) = 0.5

置換で解く

sin^{22} (x) = 0.5

仮定:

sin (x) = u

u^{22} = 0.5

u^{22} = 0.5 : u = 22 0.5, u = - 22 0.5

u^{22} = 0.5

x^{n} = f (a)

の場合, n は偶数, 解は

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

u = 22 0.5, u = - 22 0.5

代用を戻す

u = sin (x)

sin (x) = 22 0.5, sin (x) = - 22 0.5

sin (x) = 22 0.5, sin (x) = - 22 0.5

sin (x) = 22 0.5 : x = arcsin (22 0.5) + 2 πn, x = π - arcsin (22 0.5) + 2 πn

sin (x) = 22 0.5

三角関数の逆数プロパティを適用する

sin (x) = 22 0.5

以下の一般解

sin (x) = 22 0.5

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

x = arcsin (22 0.5) + 2 πn, x = π - arcsin (22 0.5) + 2 πn

x = arcsin (22 0.5) + 2 πn, x = π - arcsin (22 0.5) + 2 πn

sin (x) = - 22 0.5 : x = arcsin (- 22 0.5) + 2 πn, x = π + arcsin (22 0.5) + 2 πn

sin (x) = - 22 0.5

三角関数の逆数プロパティを適用する

sin (x) = - 22 0.5

以下の一般解

sin (x) = - 22 0.5

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

x = arcsin (- 22 0.5) + 2 πn, x = π + arcsin (22 0.5) + 2 πn

x = arcsin (- 22 0.5) + 2 πn, x = π + arcsin (22 0.5) + 2 πn

すべての解を組み合わせる

x = arcsin (22 0.5) + 2 πn, x = π - arcsin (22 0.5) + 2 πn, x = arcsin (- 22 0.5) + 2 πn, x = π + arcsin (22 0.5) + 2 πn

10進法形式で解を証明する

x = 1.32108 \dots + 2 πn, x = π - 1.32108 \dots + 2 πn, x = - 1.32108 \dots + 2 πn, x = π + 1.32108 \dots + 2 πn

グラフ

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