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人気のある三角関数 >

sin^2(x)=0.85

解

sin^{2} (x) = 0.85

解

x = 1.17309 \dots + 2 πn, x = π - 1.17309 \dots + 2 πn, x = - 1.17309 \dots + 2 πn, x = π + 1.17309 \dots + 2 πn

+1

度

x = 67.21350 \dots^{\circ} + 36 0^{\circ} n, x = 112.78649 \dots^{\circ} + 36 0^{\circ} n, x = - 67.21350 \dots^{\circ} + 36 0^{\circ} n, x = 247.21350 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

sin^{2} (x) = 0.85

置換で解く

sin^{2} (x) = 0.85

仮定:

sin (x) = u

u^{2} = 0.85

u^{2} = 0.85 : u = 0.85, u = - 0.85

u^{2} = 0.85

x^{2} = f (a)

の場合, 解は

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

u = 0.85, u = - 0.85

代用を戻す

u = sin (x)

sin (x) = 0.85, sin (x) = - 0.85

sin (x) = 0.85, sin (x) = - 0.85

sin (x) = 0.85 : x = arcsin (0.85) + 2 πn, x = π - arcsin (0.85) + 2 πn

sin (x) = 0.85

三角関数の逆数プロパティを適用する

sin (x) = 0.85

以下の一般解

sin (x) = 0.85

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

x = arcsin (0.85) + 2 πn, x = π - arcsin (0.85) + 2 πn

x = arcsin (0.85) + 2 πn, x = π - arcsin (0.85) + 2 πn

sin (x) = - 0.85 : x = arcsin (- 0.85) + 2 πn, x = π + arcsin (0.85) + 2 πn

sin (x) = - 0.85

三角関数の逆数プロパティを適用する

sin (x) = - 0.85

以下の一般解

sin (x) = - 0.85

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

x = arcsin (- 0.85) + 2 πn, x = π + arcsin (0.85) + 2 πn

x = arcsin (- 0.85) + 2 πn, x = π + arcsin (0.85) + 2 πn

すべての解を組み合わせる

x = arcsin (0.85) + 2 πn, x = π - arcsin (0.85) + 2 πn, x = arcsin (- 0.85) + 2 πn, x = π + arcsin (0.85) + 2 πn

10進法形式で解を証明する

x = 1.17309 \dots + 2 πn, x = π - 1.17309 \dots + 2 πn, x = - 1.17309 \dots + 2 πn, x = π + 1.17309 \dots + 2 πn

グラフ

人気の例

cos(x-60)=(sqrt(3))/2

cos (x - 6 0^{\circ}) = \frac{3}{2}

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(0.5 \cdot 9.8 \cdot l (1 - cos (θ))) = 0.018

solvefor x,0=-sin(2x)-2cos(x)

so l v e f or x, 0 = - sin (2 x) - 2 cos (x)

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