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人気のある三角関数 >

8cos(2x-5)=3

解

8 cos (2 x - 5) = 3

解

x = πn + \frac{5}{2} + \frac{1.18639 \dots}{2}, x = π + πn + \frac{5}{2} - \frac{1.18639 \dots}{2}

+1

度

x = 177.22729 \dots^{\circ} + 18 0^{\circ} n, x = 289.25160 \dots^{\circ} + 18 0^{\circ} n

解答ステップ

8 cos (2 x - 5) = 3

以下で両辺を割る

8

8 cos (2 x - 5) = 3

以下で両辺を割る

8

\frac{8 cos ( 2 x - 5 )}{8} = \frac{3}{8}

簡素化

cos (2 x - 5) = \frac{3}{8}

cos (2 x - 5) = \frac{3}{8}

三角関数の逆数プロパティを適用する

cos (2 x - 5) = \frac{3}{8}

以下の一般解

cos (2 x - 5) = \frac{3}{8}

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

2 x - 5 = arccos (\frac{3}{8}) + 2 πn, 2 x - 5 = 2 π - arccos (\frac{3}{8}) + 2 πn

2 x - 5 = arccos (\frac{3}{8}) + 2 πn, 2 x - 5 = 2 π - arccos (\frac{3}{8}) + 2 πn

解く

2 x - 5 = arccos (\frac{3}{8}) + 2 πn : x = πn + \frac{5}{2} + \frac{arccos ( \frac{3}{8} )}{2}

2 x - 5 = arccos (\frac{3}{8}) + 2 πn

5

を右側に移動します

2 x - 5 = arccos (\frac{3}{8}) + 2 πn

両辺に

5

を足す

2 x - 5 + 5 = arccos (\frac{3}{8}) + 2 πn + 5

簡素化

2 x = arccos (\frac{3}{8}) + 2 πn + 5

2 x = arccos (\frac{3}{8}) + 2 πn + 5

以下で両辺を割る

2

2 x = arccos (\frac{3}{8}) + 2 πn + 5

以下で両辺を割る

2

\frac{2 x}{2} = \frac{arccos ( \frac{3}{8} )}{2} + \frac{2 πn}{2} + \frac{5}{2}

簡素化

\frac{2 x}{2} = \frac{arccos ( \frac{3}{8} )}{2} + \frac{2 πn}{2} + \frac{5}{2}

簡素化

\frac{2 x}{2} : x

\frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= x

簡素化

\frac{arccos ( \frac{3}{8} )}{2} + \frac{2 πn}{2} + \frac{5}{2} : πn + \frac{5}{2} + \frac{arccos ( \frac{3}{8} )}{2}

\frac{arccos ( \frac{3}{8} )}{2} + \frac{2 πn}{2} + \frac{5}{2}

条件のようなグループ

= \frac{5}{2} + \frac{2 πn}{2} + \frac{arccos ( \frac{3}{8} )}{2}

数を割る:

\frac{2}{2} = 1

= \frac{5}{2} + πn + \frac{arccos ( \frac{3}{8} )}{2}

条件のようなグループ

= πn + \frac{5}{2} + \frac{arccos ( \frac{3}{8} )}{2}

x = πn + \frac{5}{2} + \frac{arccos ( \frac{3}{8} )}{2}

x = πn + \frac{5}{2} + \frac{arccos ( \frac{3}{8} )}{2}

x = πn + \frac{5}{2} + \frac{arccos ( \frac{3}{8} )}{2}

解く

2 x - 5 = 2 π - arccos (\frac{3}{8}) + 2 πn : x = π + πn + \frac{5}{2} - \frac{arccos ( \frac{3}{8} )}{2}

2 x - 5 = 2 π - arccos (\frac{3}{8}) + 2 πn

5

を右側に移動します

2 x - 5 = 2 π - arccos (\frac{3}{8}) + 2 πn

両辺に

5

を足す

2 x - 5 + 5 = 2 π - arccos (\frac{3}{8}) + 2 πn + 5

簡素化

2 x = 2 π - arccos (\frac{3}{8}) + 2 πn + 5

2 x = 2 π - arccos (\frac{3}{8}) + 2 πn + 5

以下で両辺を割る

2

2 x = 2 π - arccos (\frac{3}{8}) + 2 πn + 5

以下で両辺を割る

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{3}{8} )}{2} + \frac{2 πn}{2} + \frac{5}{2}

簡素化

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{3}{8} )}{2} + \frac{2 πn}{2} + \frac{5}{2}

簡素化

\frac{2 x}{2} : x

\frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= x

簡素化

\frac{2 π}{2} - \frac{arccos ( \frac{3}{8} )}{2} + \frac{2 πn}{2} + \frac{5}{2} : π + πn + \frac{5}{2} - \frac{arccos ( \frac{3}{8} )}{2}

\frac{2 π}{2} - \frac{arccos ( \frac{3}{8} )}{2} + \frac{2 πn}{2} + \frac{5}{2}

条件のようなグループ

= \frac{5}{2} + \frac{2 π}{2} + \frac{2 πn}{2} - \frac{arccos ( \frac{3}{8} )}{2}

数を割る:

\frac{2}{2} = 1

= \frac{5}{2} + π + πn - \frac{arccos ( \frac{3}{8} )}{2}

条件のようなグループ

= π + πn + \frac{5}{2} - \frac{arccos ( \frac{3}{8} )}{2}

x = π + πn + \frac{5}{2} - \frac{arccos ( \frac{3}{8} )}{2}

x = π + πn + \frac{5}{2} - \frac{arccos ( \frac{3}{8} )}{2}

x = π + πn + \frac{5}{2} - \frac{arccos ( \frac{3}{8} )}{2}

x = πn + \frac{5}{2} + \frac{arccos ( \frac{3}{8} )}{2}, x = π + πn + \frac{5}{2} - \frac{arccos ( \frac{3}{8} )}{2}

10進法形式で解を証明する

x = πn + \frac{5}{2} + \frac{1.18639 \dots}{2}, x = π + πn + \frac{5}{2} - \frac{1.18639 \dots}{2}

グラフ

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