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人気のある三角関数 >

cos(2x+15)=0.3

解

cos (2 x + 15) = 0.3

解

x = πn - \frac{15}{2} + \frac{1.26610 \dots}{2}, x = π + πn - \frac{15}{2} - \frac{1.26610 \dots}{2}

+1

度

x = - 393.44714 \dots^{\circ} + 18 0^{\circ} n, x = - 285.98954 \dots^{\circ} + 18 0^{\circ} n

解答ステップ

cos (2 x + 15) = 0.3

三角関数の逆数プロパティを適用する

cos (2 x + 15) = 0.3

以下の一般解

cos (2 x + 15) = 0.3

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

2 x + 15 = arccos (0.3) + 2 πn, 2 x + 15 = 2 π - arccos (0.3) + 2 πn

2 x + 15 = arccos (0.3) + 2 πn, 2 x + 15 = 2 π - arccos (0.3) + 2 πn

解く

2 x + 15 = arccos (0.3) + 2 πn : x = πn - \frac{15}{2} + \frac{arccos ( 0.3 )}{2}

2 x + 15 = arccos (0.3) + 2 πn

15

を右側に移動します

2 x + 15 = arccos (0.3) + 2 πn

両辺から

15

を引く

2 x + 15 - 15 = arccos (0.3) + 2 πn - 15

簡素化

2 x = arccos (0.3) + 2 πn - 15

2 x = arccos (0.3) + 2 πn - 15

以下で両辺を割る

2

2 x = arccos (0.3) + 2 πn - 15

以下で両辺を割る

2

\frac{2 x}{2} = \frac{arccos ( 0.3 )}{2} + \frac{2 πn}{2} - \frac{15}{2}

簡素化

\frac{2 x}{2} = \frac{arccos ( 0.3 )}{2} + \frac{2 πn}{2} - \frac{15}{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 ( 0.3 )}{2} + \frac{2 πn}{2} - \frac{15}{2} : πn - \frac{15}{2} + \frac{arccos ( 0.3 )}{2}

\frac{arccos ( 0.3 )}{2} + \frac{2 πn}{2} - \frac{15}{2}

条件のようなグループ

= - \frac{15}{2} + \frac{2 πn}{2} + \frac{arccos ( 0.3 )}{2}

数を割る:

\frac{2}{2} = 1

= - \frac{15}{2} + πn + \frac{arccos ( 0.3 )}{2}

条件のようなグループ

= πn - \frac{15}{2} + \frac{arccos ( 0.3 )}{2}

x = πn - \frac{15}{2} + \frac{arccos ( 0.3 )}{2}

x = πn - \frac{15}{2} + \frac{arccos ( 0.3 )}{2}

x = πn - \frac{15}{2} + \frac{arccos ( 0.3 )}{2}

解く

2 x + 15 = 2 π - arccos (0.3) + 2 πn : x = π + πn - \frac{15}{2} - \frac{arccos ( 0.3 )}{2}

2 x + 15 = 2 π - arccos (0.3) + 2 πn

15

を右側に移動します

2 x + 15 = 2 π - arccos (0.3) + 2 πn

両辺から

15

を引く

2 x + 15 - 15 = 2 π - arccos (0.3) + 2 πn - 15

簡素化

2 x = 2 π - arccos (0.3) + 2 πn - 15

2 x = 2 π - arccos (0.3) + 2 πn - 15

以下で両辺を割る

2

2 x = 2 π - arccos (0.3) + 2 πn - 15

以下で両辺を割る

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( 0.3 )}{2} + \frac{2 πn}{2} - \frac{15}{2}

簡素化

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( 0.3 )}{2} + \frac{2 πn}{2} - \frac{15}{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 ( 0.3 )}{2} + \frac{2 πn}{2} - \frac{15}{2} : π + πn - \frac{15}{2} - \frac{arccos ( 0.3 )}{2}

\frac{2 π}{2} - \frac{arccos ( 0.3 )}{2} + \frac{2 πn}{2} - \frac{15}{2}

条件のようなグループ

= \frac{2 π}{2} - \frac{15}{2} + \frac{2 πn}{2} - \frac{arccos ( 0.3 )}{2}

数を割る:

\frac{2}{2} = 1

= π - \frac{15}{2} + πn - \frac{arccos ( 0.3 )}{2}

条件のようなグループ

= π + πn - \frac{15}{2} - \frac{arccos ( 0.3 )}{2}

x = π + πn - \frac{15}{2} - \frac{arccos ( 0.3 )}{2}

x = π + πn - \frac{15}{2} - \frac{arccos ( 0.3 )}{2}

x = π + πn - \frac{15}{2} - \frac{arccos ( 0.3 )}{2}

x = πn - \frac{15}{2} + \frac{arccos ( 0.3 )}{2}, x = π + πn - \frac{15}{2} - \frac{arccos ( 0.3 )}{2}

10進法形式で解を証明する

x = πn - \frac{15}{2} + \frac{1.26610 \dots}{2}, x = π + πn - \frac{15}{2} - \frac{1.26610 \dots}{2}

グラフ

人気の例

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