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人気のある三角関数 >

solvefor x,cos^2(x)=0.5

解

解く

x, cos^{2} (x) = 0.5

解

x = 0.78539 \dots + 2 πn, x = 2 π - 0.78539 \dots + 2 πn, x = 2.35619 \dots + 2 πn, x = - 2.35619 \dots + 2 πn

+1

度

x = 4 5^{\circ} + 36 0^{\circ} n, x = 31 5^{\circ} + 36 0^{\circ} n, x = 13 5^{\circ} + 36 0^{\circ} n, x = - 13 5^{\circ} + 36 0^{\circ} n

解答ステップ

cos^{2} (x) = 0.5

置換で解く

cos^{2} (x) = 0.5

仮定:

cos (x) = u

u^{2} = 0.5

u^{2} = 0.5 : u = 0.5, u = - 0.5

u^{2} = 0.5

x^{2} = f (a)

の場合, 解は

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

u = 0.5, u = - 0.5

代用を戻す

u = cos (x)

cos (x) = 0.5, cos (x) = - 0.5

cos (x) = 0.5, cos (x) = - 0.5

cos (x) = 0.5 : x = arccos (0.5) + 2 πn, x = 2 π - arccos (0.5) + 2 πn

cos (x) = 0.5

三角関数の逆数プロパティを適用する

cos (x) = 0.5

以下の一般解

cos (x) = 0.5

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

x = arccos (0.5) + 2 πn, x = 2 π - arccos (0.5) + 2 πn

x = arccos (0.5) + 2 πn, x = 2 π - arccos (0.5) + 2 πn

cos (x) = - 0.5 : x = arccos (- 0.5) + 2 πn, x = - arccos (- 0.5) + 2 πn

cos (x) = - 0.5

三角関数の逆数プロパティを適用する

cos (x) = - 0.5

以下の一般解

cos (x) = - 0.5

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

x = arccos (- 0.5) + 2 πn, x = - arccos (- 0.5) + 2 πn

x = arccos (- 0.5) + 2 πn, x = - arccos (- 0.5) + 2 πn

すべての解を組み合わせる

x = arccos (0.5) + 2 πn, x = 2 π - arccos (0.5) + 2 πn, x = arccos (- 0.5) + 2 πn, x = - arccos (- 0.5) + 2 πn

10進法形式で解を証明する

x = 0.78539 \dots + 2 πn, x = 2 π - 0.78539 \dots + 2 πn, x = 2.35619 \dots + 2 πn, x = - 2.35619 \dots + 2 πn

グラフ

人気の例

sin(x)=0.24,0<= x<2pi

sin (x) = 0.24, 0 \leq x < 2 π

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sec^{2} (θ) cot (θ) = 8

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