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人気のある三角関数 >

6cos(6x)=5

解

6 cos (6 x) = 5

解

x = \frac{0.58568 \dots}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{0.58568 \dots}{6} + \frac{πn}{3}

+1

度

x = 5.59288 \dots^{\circ} + 6 0^{\circ} n, x = 54.40711 \dots^{\circ} + 6 0^{\circ} n

解答ステップ

6 cos (6 x) = 5

以下で両辺を割る

6

6 cos (6 x) = 5

以下で両辺を割る

6

\frac{6 cos ( 6 x )}{6} = \frac{5}{6}

簡素化

cos (6 x) = \frac{5}{6}

cos (6 x) = \frac{5}{6}

三角関数の逆数プロパティを適用する

cos (6 x) = \frac{5}{6}

以下の一般解

cos (6 x) = \frac{5}{6}

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

6 x = arccos (\frac{5}{6}) + 2 πn, 6 x = 2 π - arccos (\frac{5}{6}) + 2 πn

6 x = arccos (\frac{5}{6}) + 2 πn, 6 x = 2 π - arccos (\frac{5}{6}) + 2 πn

解く

6 x = arccos (\frac{5}{6}) + 2 πn : x = \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}

6 x = arccos (\frac{5}{6}) + 2 πn

以下で両辺を割る

6

6 x = arccos (\frac{5}{6}) + 2 πn

以下で両辺を割る

6

\frac{6 x}{6} = \frac{arccos ( \frac{5}{6} )}{6} + \frac{2 πn}{6}

簡素化

x = \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}

x = \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}

解く

6 x = 2 π - arccos (\frac{5}{6}) + 2 πn : x = \frac{π}{3} - \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}

6 x = 2 π - arccos (\frac{5}{6}) + 2 πn

以下で両辺を割る

6

6 x = 2 π - arccos (\frac{5}{6}) + 2 πn

以下で両辺を割る

6

\frac{6 x}{6} = \frac{2 π}{6} - \frac{arccos ( \frac{5}{6} )}{6} + \frac{2 πn}{6}

簡素化

\frac{6 x}{6} = \frac{2 π}{6} - \frac{arccos ( \frac{5}{6} )}{6} + \frac{2 πn}{6}

簡素化

\frac{6 x}{6} : x

\frac{6 x}{6}

数を割る:

\frac{6}{6} = 1

= x

簡素化

\frac{2 π}{6} - \frac{arccos ( \frac{5}{6} )}{6} + \frac{2 πn}{6} : \frac{π}{3} - \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}

\frac{2 π}{6} - \frac{arccos ( \frac{5}{6} )}{6} + \frac{2 πn}{6}

キャンセル

\frac{2 π}{6} : \frac{π}{3}

\frac{2 π}{6}

共通因数を約分する:

2

= \frac{π}{3}

= \frac{π}{3} - \frac{arccos ( \frac{5}{6} )}{6} + \frac{2 πn}{6}

キャンセル

\frac{2 πn}{6} : \frac{πn}{3}

\frac{2 πn}{6}

共通因数を約分する:

2

= \frac{πn}{3}

= \frac{π}{3} - \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}

x = \frac{π}{3} - \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}

x = \frac{π}{3} - \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}

x = \frac{π}{3} - \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}

x = \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{arccos ( \frac{5}{6} )}{6} + \frac{πn}{3}

10進法形式で解を証明する

x = \frac{0.58568 \dots}{6} + \frac{πn}{3}, x = \frac{π}{3} - \frac{0.58568 \dots}{6} + \frac{πn}{3}

グラフ

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