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人気のある三角関数 >

0.08=0.12cos^2(3.922t)

解

0.08 = 0.12 cos^{2} (3.922 t)

解

t = \frac{0.61547 \dots}{3.922} + \frac{2 πn}{3.922}, t = \frac{2 π}{3.922} - \frac{0.61547 \dots}{3.922} + \frac{2 πn}{3.922}, t = \frac{2.52611 \dots}{3.922} + \frac{2 πn}{3.922}, t = - \frac{2.52611 \dots}{3.922} + \frac{2 πn}{3.922}

+1

度

t = 8.99143 \dots^{\circ} + 91.78990 \dots^{\circ} n, t = 82.79847 \dots^{\circ} + 91.78990 \dots^{\circ} n, t = 36.90352 \dots^{\circ} + 91.78990 \dots^{\circ} n, t = - 36.90352 \dots^{\circ} + 91.78990 \dots^{\circ} n

解答ステップ

0.08 = 0.12 cos^{2} (3.922 t)

辺を交換する

0.12 cos^{2} (3.922 t) = 0.08

置換で解く

0.12 cos^{2} (3.922 t) = 0.08

仮定:

cos (3.922 t) = u

0.12 u^{2} = 0.08

0.12 u^{2} = 0.08 : u = \frac{2}{3}, u = - \frac{2}{3}

0.12 u^{2} = 0.08

以下で両辺を乗じる:

100

0.12 u^{2} = 0.08

小数点を取り除くには, 小数点以下の各桁に10を乗じます小数点の右側は

2

桁なので,

100 を乗じます

0.12 u^{2} \cdot 100 = 0.08 \cdot 100

改良

12 u^{2} = 8

12 u^{2} = 8

以下で両辺を割る

12

12 u^{2} = 8

以下で両辺を割る

12

\frac{12 u ^{2}}{12} = \frac{8}{12}

簡素化

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

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

x^{2} = f (a)

の場合, 解は

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

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

代用を戻す

u = cos (3.922 t)

cos (3.922 t) = \frac{2}{3}, cos (3.922 t) = - \frac{2}{3}

cos (3.922 t) = \frac{2}{3}, cos (3.922 t) = - \frac{2}{3}

cos (3.922 t) = \frac{2}{3} : t = \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}, t = \frac{2 π}{3.922} - \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

cos (3.922 t) = \frac{2}{3}

三角関数の逆数プロパティを適用する

cos (3.922 t) = \frac{2}{3}

以下の一般解

cos (3.922 t) = \frac{2}{3}

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

3.922 t = arccos (\frac{2}{3}) + 2 πn, 3.922 t = 2 π - arccos (\frac{2}{3}) + 2 πn

3.922 t = arccos (\frac{2}{3}) + 2 πn, 3.922 t = 2 π - arccos (\frac{2}{3}) + 2 πn

解く

3.922 t = arccos (\frac{2}{3}) + 2 πn : t = \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

3.922 t = arccos (\frac{2}{3}) + 2 πn

以下で両辺を割る

3.922

3.922 t = arccos (\frac{2}{3}) + 2 πn

以下で両辺を割る

3.922

\frac{3.922 t}{3.922} = \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

簡素化

t = \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

t = \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

解く

3.922 t = 2 π - arccos (\frac{2}{3}) + 2 πn : t = \frac{2 π}{3.922} - \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

3.922 t = 2 π - arccos (\frac{2}{3}) + 2 πn

以下で両辺を割る

3.922

3.922 t = 2 π - arccos (\frac{2}{3}) + 2 πn

以下で両辺を割る

3.922

\frac{3.922 t}{3.922} = \frac{2 π}{3.922} - \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

簡素化

t = \frac{2 π}{3.922} - \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

t = \frac{2 π}{3.922} - \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

t = \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}, t = \frac{2 π}{3.922} - \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

cos (3.922 t) = - \frac{2}{3} : t = \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}, t = - \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

cos (3.922 t) = - \frac{2}{3}

三角関数の逆数プロパティを適用する

cos (3.922 t) = - \frac{2}{3}

以下の一般解

cos (3.922 t) = - \frac{2}{3}

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

3.922 t = arccos (- \frac{2}{3}) + 2 πn, 3.922 t = - arccos (- \frac{2}{3}) + 2 πn

3.922 t = arccos (- \frac{2}{3}) + 2 πn, 3.922 t = - arccos (- \frac{2}{3}) + 2 πn

解く

3.922 t = arccos (- \frac{2}{3}) + 2 πn : t = \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

3.922 t = arccos (- \frac{2}{3}) + 2 πn

以下で両辺を割る

3.922

3.922 t = arccos (- \frac{2}{3}) + 2 πn

以下で両辺を割る

3.922

\frac{3.922 t}{3.922} = \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

簡素化

t = \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

t = \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

解く

3.922 t = - arccos (- \frac{2}{3}) + 2 πn : t = - \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

3.922 t = - arccos (- \frac{2}{3}) + 2 πn

以下で両辺を割る

3.922

3.922 t = - arccos (- \frac{2}{3}) + 2 πn

以下で両辺を割る

3.922

\frac{3.922 t}{3.922} = - \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

簡素化

t = - \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

t = - \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

t = \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}, t = - \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

すべての解を組み合わせる

t = \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}, t = \frac{2 π}{3.922} - \frac{arccos ( \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}, t = \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}, t = - \frac{arccos ( - \frac{2}{3} )}{3.922} + \frac{2 πn}{3.922}

10進法形式で解を証明する

t = \frac{0.61547 \dots}{3.922} + \frac{2 πn}{3.922}, t = \frac{2 π}{3.922} - \frac{0.61547 \dots}{3.922} + \frac{2 πn}{3.922}, t = \frac{2.52611 \dots}{3.922} + \frac{2 πn}{3.922}, t = - \frac{2.52611 \dots}{3.922} + \frac{2 πn}{3.922}

グラフ

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