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人気のある三角関数 >

cos^2(x)= 9/16

解

cos^{2} (x) = \frac{9}{16}

解

x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn, x = 2.41885 \dots + 2 πn, x = - 2.41885 \dots + 2 πn

+1

度

x = 41.40962 \dots^{\circ} + 36 0^{\circ} n, x = 318.59037 \dots^{\circ} + 36 0^{\circ} n, x = 138.59037 \dots^{\circ} + 36 0^{\circ} n, x = - 138.59037 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

cos^{2} (x) = \frac{9}{16}

置換で解く

cos^{2} (x) = \frac{9}{16}

仮定:

cos (x) = u

u^{2} = \frac{9}{16}

u^{2} = \frac{9}{16} : u = \frac{3}{4}, u = - \frac{3}{4}

u^{2} = \frac{9}{16}

x^{2} = f (a)

の場合, 解は

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

u = \frac{9}{16}, u = - \frac{9}{16}

\frac{9}{16} = \frac{3}{4}

\frac{9}{16}

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{9}{16}

16 = 4

16

数を因数に分解する:

16 = 4^{2}

= 4^{2}

累乗根の規則を適用する:

n a^{n} = a

4^{2} = 4

= 4

= \frac{9}{4}

9 = 3

9

数を因数に分解する:

9 = 3^{2}

= 3^{2}

累乗根の規則を適用する:

n a^{n} = a

3^{2} = 3

= 3

= \frac{3}{4}

- \frac{9}{16} = - \frac{3}{4}

- \frac{9}{16}

簡素化

\frac{9}{16} : \frac{3}{4}

\frac{9}{16}

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{9}{16}

16 = 4

16

数を因数に分解する:

16 = 4^{2}

= 4^{2}

累乗根の規則を適用する:

n a^{n} = a

4^{2} = 4

= 4

= \frac{9}{4}

9 = 3

9

数を因数に分解する:

9 = 3^{2}

= 3^{2}

累乗根の規則を適用する:

n a^{n} = a

3^{2} = 3

= 3

= \frac{3}{4}

= - \frac{3}{4}

u = \frac{3}{4}, u = - \frac{3}{4}

代用を戻す

u = cos (x)

cos (x) = \frac{3}{4}, cos (x) = - \frac{3}{4}

cos (x) = \frac{3}{4}, cos (x) = - \frac{3}{4}

cos (x) = \frac{3}{4} : x = arccos (\frac{3}{4}) + 2 πn, x = 2 π - arccos (\frac{3}{4}) + 2 πn

cos (x) = \frac{3}{4}

三角関数の逆数プロパティを適用する

cos (x) = \frac{3}{4}

以下の一般解

cos (x) = \frac{3}{4}

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

x = arccos (\frac{3}{4}) + 2 πn, x = 2 π - arccos (\frac{3}{4}) + 2 πn

x = arccos (\frac{3}{4}) + 2 πn, x = 2 π - arccos (\frac{3}{4}) + 2 πn

cos (x) = - \frac{3}{4} : x = arccos (- \frac{3}{4}) + 2 πn, x = - arccos (- \frac{3}{4}) + 2 πn

cos (x) = - \frac{3}{4}

三角関数の逆数プロパティを適用する

cos (x) = - \frac{3}{4}

以下の一般解

cos (x) = - \frac{3}{4}

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

x = arccos (- \frac{3}{4}) + 2 πn, x = - arccos (- \frac{3}{4}) + 2 πn

x = arccos (- \frac{3}{4}) + 2 πn, x = - arccos (- \frac{3}{4}) + 2 πn

すべての解を組み合わせる

x = arccos (\frac{3}{4}) + 2 πn, x = 2 π - arccos (\frac{3}{4}) + 2 πn, x = arccos (- \frac{3}{4}) + 2 πn, x = - arccos (- \frac{3}{4}) + 2 πn

10進法形式で解を証明する

x = 0.72273 \dots + 2 πn, x = 2 π - 0.72273 \dots + 2 πn, x = 2.41885 \dots + 2 πn, x = - 2.41885 \dots + 2 πn

グラフ

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