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人気のある三角関数 >

cos^2(x)= pi/4

解

cos^{2} (x) = \frac{π}{4}

解

x = 0.48166 \dots + 2 πn, x = 2 π - 0.48166 \dots + 2 πn, x = 2.65993 \dots + 2 πn, x = - 2.65993 \dots + 2 πn

+1

度

x = 27.59711 \dots^{\circ} + 36 0^{\circ} n, x = 332.40288 \dots^{\circ} + 36 0^{\circ} n, x = 152.40288 \dots^{\circ} + 36 0^{\circ} n, x = - 152.40288 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

cos^{2} (x) = \frac{π}{4}

置換で解く

cos^{2} (x) = \frac{π}{4}

仮定:

cos (x) = u

u^{2} = \frac{π}{4}

u^{2} = \frac{π}{4} : u = \frac{π}{2}, u = - \frac{π}{2}

u^{2} = \frac{π}{4}

x^{2} = f (a)

の場合, 解は

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

u = \frac{π}{4}, u = - \frac{π}{4}

\frac{π}{4} = \frac{π}{2}

\frac{π}{4}

累乗根の規則を適用する:

n \frac{a}{b} = \frac{n a}{n b},

, 以下を想定

a \geq 0, b \geq 0

= \frac{π}{4}

4 = 2

4

数を因数に分解する:

4 = 2^{2}

= 2^{2}

累乗根の規則を適用する:

n a^{n} = a

2^{2} = 2

= 2

= \frac{π}{2}

- \frac{π}{4} = - \frac{π}{2}

- \frac{π}{4}

簡素化

\frac{π}{4} : \frac{π}{2}

\frac{π}{4}

累乗根の規則を適用する:

n \frac{a}{b} = \frac{n a}{n b},

, 以下を想定

a \geq 0, b \geq 0

= \frac{π}{4}

4 = 2

4

数を因数に分解する:

4 = 2^{2}

= 2^{2}

累乗根の規則を適用する:

n a^{n} = a

2^{2} = 2

= 2

= \frac{π}{2}

= - \frac{π}{2}

u = \frac{π}{2}, u = - \frac{π}{2}

代用を戻す

u = cos (x)

cos (x) = \frac{π}{2}, cos (x) = - \frac{π}{2}

cos (x) = \frac{π}{2}, cos (x) = - \frac{π}{2}

cos (x) = \frac{π}{2} : x = arccos (\frac{π}{2}) + 2 πn, x = 2 π - arccos (\frac{π}{2}) + 2 πn

cos (x) = \frac{π}{2}

三角関数の逆数プロパティを適用する

cos (x) = \frac{π}{2}

以下の一般解

cos (x) = \frac{π}{2}

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

x = arccos (\frac{π}{2}) + 2 πn, x = 2 π - arccos (\frac{π}{2}) + 2 πn

x = arccos (\frac{π}{2}) + 2 πn, x = 2 π - arccos (\frac{π}{2}) + 2 πn

cos (x) = - \frac{π}{2} : x = arccos (- \frac{π}{2}) + 2 πn, x = - arccos (- \frac{π}{2}) + 2 πn

cos (x) = - \frac{π}{2}

三角関数の逆数プロパティを適用する

cos (x) = - \frac{π}{2}

以下の一般解

cos (x) = - \frac{π}{2}

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

x = arccos (- \frac{π}{2}) + 2 πn, x = - arccos (- \frac{π}{2}) + 2 πn

x = arccos (- \frac{π}{2}) + 2 πn, x = - arccos (- \frac{π}{2}) + 2 πn

すべての解を組み合わせる

x = arccos (\frac{π}{2}) + 2 πn, x = 2 π - arccos (\frac{π}{2}) + 2 πn, x = arccos (- \frac{π}{2}) + 2 πn, x = - arccos (- \frac{π}{2}) + 2 πn

10進法形式で解を証明する

x = 0.48166 \dots + 2 πn, x = 2 π - 0.48166 \dots + 2 πn, x = 2.65993 \dots + 2 πn, x = - 2.65993 \dots + 2 πn

グラフ

人気の例

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cot^{2} (θ) + csc (θ) = 1, 0 \leq θ < 2 π

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