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人気のある三角関数 >

3cos(5x)=2

解

3 cos (5 x) = 2

解

x = \frac{0.84106 \dots}{5} + \frac{2 πn}{5}, x = \frac{2 π}{5} - \frac{0.84106 \dots}{5} + \frac{2 πn}{5}

+1

度

x = 9.63793 \dots^{\circ} + 7 2^{\circ} n, x = 62.36206 \dots^{\circ} + 7 2^{\circ} n

解答ステップ

3 cos (5 x) = 2

以下で両辺を割る

3

3 cos (5 x) = 2

以下で両辺を割る

3

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

簡素化

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

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

三角関数の逆数プロパティを適用する

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

以下の一般解

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

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

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

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

解く

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

5 x = arccos (\frac{2}{3}) + 2 πn

以下で両辺を割る

5

5 x = arccos (\frac{2}{3}) + 2 πn

以下で両辺を割る

5

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

簡素化

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

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

解く

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

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

以下で両辺を割る

5

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

以下で両辺を割る

5

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

簡素化

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

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

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

10進法形式で解を証明する

x = \frac{0.84106 \dots}{5} + \frac{2 πn}{5}, x = \frac{2 π}{5} - \frac{0.84106 \dots}{5} + \frac{2 πn}{5}

グラフ

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