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人気のある三角関数 >

4.797896cos(0.568x-2.595)=0

解

4.797896 cos (0.568 x - 2.595) = 0

解

x = \frac{125 π}{142} + \frac{2595}{568} + \frac{250 πn}{71}, x = \frac{2595}{568} + \frac{375 π}{142} + \frac{250 πn}{71}

+1

度

x = 420.21575 \dots^{\circ} + 633.80281 \dots^{\circ} n, x = 737.11716 \dots^{\circ} + 633.80281 \dots^{\circ} n

解答ステップ

4.797896 cos (0.568 x - 2.595) = 0

以下で両辺を割る

4.797896

4.797896 cos (0.568 x - 2.595) = 0

以下で両辺を割る

4.797896

\frac{4.797896 cos ( 0.568 x - 2.595 )}{4.797896} = \frac{0}{4.797896}

簡素化

cos (0.568 x - 2.595) = 0

cos (0.568 x - 2.595) = 0

以下の一般解

cos (0.568 x - 2.595) = 0

cos (x)

2 πn

循環を含む周期性テーブル:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

0.568 x - 2.595 = \frac{π}{2} + 2 πn, 0.568 x - 2.595 = \frac{3 π}{2} + 2 πn

0.568 x - 2.595 = \frac{π}{2} + 2 πn, 0.568 x - 2.595 = \frac{3 π}{2} + 2 πn

解く

0.568 x - 2.595 = \frac{π}{2} + 2 πn : x = \frac{125 π}{142} + \frac{2595}{568} + \frac{250 πn}{71}

0.568 x - 2.595 = \frac{π}{2} + 2 πn

以下で両辺を乗じる:

1000

0.568 x - 2.595 = \frac{π}{2} + 2 πn

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

3

桁なので,

1000 を乗じます

0.568 x \cdot 1000 - 2.595 \cdot 1000 = \frac{π}{2} \cdot 1000 + 2 πn \cdot 1000

改良

568 x - 2595 = 500 π + 2000 πn

568 x - 2595 = 500 π + 2000 πn

2595

を右側に移動します

568 x - 2595 = 500 π + 2000 πn

両辺に

2595

を足す

568 x - 2595 + 2595 = 500 π + 2000 πn + 2595

簡素化

568 x = 500 π + 2000 πn + 2595

568 x = 500 π + 2000 πn + 2595

以下で両辺を割る

568

568 x = 500 π + 2000 πn + 2595

以下で両辺を割る

568

\frac{568 x}{568} = \frac{500 π}{568} + \frac{2000 πn}{568} + \frac{2595}{568}

簡素化

\frac{568 x}{568} = \frac{500 π}{568} + \frac{2000 πn}{568} + \frac{2595}{568}

簡素化

\frac{568 x}{568} : x

\frac{568 x}{568}

数を割る:

\frac{568}{568} = 1

= x

簡素化

\frac{500 π}{568} + \frac{2000 πn}{568} + \frac{2595}{568} : \frac{125 π}{142} + \frac{2595}{568} + \frac{250 πn}{71}

\frac{500 π}{568} + \frac{2000 πn}{568} + \frac{2595}{568}

条件のようなグループ

= \frac{500 π}{568} + \frac{2595}{568} + \frac{2000 πn}{568}

キャンセル

\frac{500 π}{568} : \frac{125 π}{142}

\frac{500 π}{568}

共通因数を約分する:

4

= \frac{125 π}{142}

= \frac{125 π}{142} + \frac{2595}{568} + \frac{2000 πn}{568}

キャンセル

\frac{2000 πn}{568} : \frac{250 πn}{71}

\frac{2000 πn}{568}

共通因数を約分する:

8

= \frac{250 πn}{71}

= \frac{125 π}{142} + \frac{2595}{568} + \frac{250 πn}{71}

x = \frac{125 π}{142} + \frac{2595}{568} + \frac{250 πn}{71}

x = \frac{125 π}{142} + \frac{2595}{568} + \frac{250 πn}{71}

x = \frac{125 π}{142} + \frac{2595}{568} + \frac{250 πn}{71}

解く

0.568 x - 2.595 = \frac{3 π}{2} + 2 πn : x = \frac{2595}{568} + \frac{375 π}{142} + \frac{250 πn}{71}

0.568 x - 2.595 = \frac{3 π}{2} + 2 πn

以下で両辺を乗じる:

1000

0.568 x - 2.595 = \frac{3 π}{2} + 2 πn

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

3

桁なので,

1000 を乗じます

0.568 x \cdot 1000 - 2.595 \cdot 1000 = \frac{3 π}{2} \cdot 1000 + 2 πn \cdot 1000

改良

568 x - 2595 = 1500 π + 2000 πn

568 x - 2595 = 1500 π + 2000 πn

2595

を右側に移動します

568 x - 2595 = 1500 π + 2000 πn

両辺に

2595

を足す

568 x - 2595 + 2595 = 1500 π + 2000 πn + 2595

簡素化

568 x = 1500 π + 2000 πn + 2595

568 x = 1500 π + 2000 πn + 2595

以下で両辺を割る

568

568 x = 1500 π + 2000 πn + 2595

以下で両辺を割る

568

\frac{568 x}{568} = \frac{1500 π}{568} + \frac{2000 πn}{568} + \frac{2595}{568}

簡素化

\frac{568 x}{568} = \frac{1500 π}{568} + \frac{2000 πn}{568} + \frac{2595}{568}

簡素化

\frac{568 x}{568} : x

\frac{568 x}{568}

数を割る:

\frac{568}{568} = 1

= x

簡素化

\frac{1500 π}{568} + \frac{2000 πn}{568} + \frac{2595}{568} : \frac{2595}{568} + \frac{375 π}{142} + \frac{250 πn}{71}

\frac{1500 π}{568} + \frac{2000 πn}{568} + \frac{2595}{568}

条件のようなグループ

= \frac{2595}{568} + \frac{1500 π}{568} + \frac{2000 πn}{568}

キャンセル

\frac{1500 π}{568} : \frac{375 π}{142}

\frac{1500 π}{568}

共通因数を約分する:

4

= \frac{375 π}{142}

= \frac{2595}{568} + \frac{375 π}{142} + \frac{2000 πn}{568}

キャンセル

\frac{2000 πn}{568} : \frac{250 πn}{71}

\frac{2000 πn}{568}

共通因数を約分する:

8

= \frac{250 πn}{71}

= \frac{2595}{568} + \frac{375 π}{142} + \frac{250 πn}{71}

x = \frac{2595}{568} + \frac{375 π}{142} + \frac{250 πn}{71}

x = \frac{2595}{568} + \frac{375 π}{142} + \frac{250 πn}{71}

x = \frac{2595}{568} + \frac{375 π}{142} + \frac{250 πn}{71}

x = \frac{125 π}{142} + \frac{2595}{568} + \frac{250 πn}{71}, x = \frac{2595}{568} + \frac{375 π}{142} + \frac{250 πn}{71}

グラフ

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