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人気のある三角関数 >

sin^2(x)=((sqrt(3)))/2

解

sin^{2} (x) = \frac{( 3 )}{2}

解

x = 1.19606 \dots + 2 πn, x = π - 1.19606 \dots + 2 πn, x = - 1.19606 \dots + 2 πn, x = π + 1.19606 \dots + 2 πn

+1

度

x = 68.52929 \dots^{\circ} + 36 0^{\circ} n, x = 111.47070 \dots^{\circ} + 36 0^{\circ} n, x = - 68.52929 \dots^{\circ} + 36 0^{\circ} n, x = 248.52929 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

sin^{2} (x) = \frac{( 3 )}{2}

置換で解く

sin^{2} (x) = \frac{3}{2}

仮定:

sin (x) = u

u^{2} = \frac{3}{2}

u^{2} = \frac{3}{2} : u = \frac{3}{2}, u = - \frac{3}{2}

u^{2} = \frac{3}{2}

x^{2} = f (a)

の場合, 解は

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

u = \frac{3}{2}, u = - \frac{3}{2}

代用を戻す

u = sin (x)

sin (x) = \frac{3}{2}, sin (x) = - \frac{3}{2}

sin (x) = \frac{3}{2}, sin (x) = - \frac{3}{2}

sin (x) = \frac{3}{2} : x = arcsin \frac{3}{2} + 2 πn, x = π - arcsin \frac{3}{2} + 2 πn

sin (x) = \frac{3}{2}

三角関数の逆数プロパティを適用する

sin (x) = \frac{3}{2}

以下の一般解

sin (x) = \frac{3}{2}

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

x = arcsin \frac{3}{2} + 2 πn, x = π - arcsin \frac{3}{2} + 2 πn

x = arcsin \frac{3}{2} + 2 πn, x = π - arcsin \frac{3}{2} + 2 πn

sin (x) = - \frac{3}{2} : x = arcsin - \frac{3}{2} + 2 πn, x = π + arcsin \frac{3}{2} + 2 πn

sin (x) = - \frac{3}{2}

三角関数の逆数プロパティを適用する

sin (x) = - \frac{3}{2}

以下の一般解

sin (x) = - \frac{3}{2}

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

x = arcsin - \frac{3}{2} + 2 πn, x = π + arcsin \frac{3}{2} + 2 πn

x = arcsin - \frac{3}{2} + 2 πn, x = π + arcsin \frac{3}{2} + 2 πn

すべての解を組み合わせる

x = arcsin \frac{3}{2} + 2 πn, x = π - arcsin \frac{3}{2} + 2 πn, x = arcsin - \frac{3}{2} + 2 πn, x = π + arcsin \frac{3}{2} + 2 πn

10進法形式で解を証明する

x = 1.19606 \dots + 2 πn, x = π - 1.19606 \dots + 2 πn, x = - 1.19606 \dots + 2 πn, x = π + 1.19606 \dots + 2 πn

グラフ

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