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人気のある三角関数 >

11.33=1.59cos(0.99(x-182))+12.14

解

11.33 = 1.59 cos (0.9 9^{\circ} (x - 18 2^{\circ})) + 12.14

解

x = 18 2^{\circ} + \frac{4000 n}{11} + \frac{2000 \cdot 2.10532 \dots}{198 0 ^{\circ}}, x = 18 2^{\circ} + \frac{4000 n}{11} - \frac{2000 \cdot 2.10532 \dots}{198 0 ^{\circ}}

+1

ラジアン

x = \frac{91 π}{90} + \frac{2000 \cdot 2.10532 \dots}{11 π} + \frac{4000}{11} n, x = \frac{91 π}{90} - \frac{2000 \cdot 2.10532 \dots}{11 π} + \frac{4000}{11} n

解答ステップ

11.33 = 1.59 cos (0.9 9^{\circ} (x - 18 2^{\circ})) + 12.14

辺を交換する

1.59 cos (0.9 9^{\circ} (x - 18 2^{\circ})) + 12.14 = 11.33

以下で両辺を乗じる:

100

1.59 cos (0.9 9^{\circ} (x - 18 2^{\circ})) + 12.14 = 11.33

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

2

桁なので,

100 を乗じます

1.59 cos (0.9 9^{\circ} (x - 18 2^{\circ})) \cdot 100 + 12.14 \cdot 100 = 11.33 \cdot 100

改良

159 cos (0.9 9^{\circ} (x - 18 2^{\circ})) + 1214 = 1133

159 cos (0.9 9^{\circ} (x - 18 2^{\circ})) + 1214 = 1133

1214

を右側に移動します

159 cos (0.9 9^{\circ} (x - 18 2^{\circ})) + 1214 = 1133

両辺から

1214

を引く

159 cos (0.9 9^{\circ} (x - 18 2^{\circ})) + 1214 - 1214 = 1133 - 1214

簡素化

159 cos (0.9 9^{\circ} (x - 18 2^{\circ})) = - 81

159 cos (0.9 9^{\circ} (x - 18 2^{\circ})) = - 81

以下で両辺を割る

159

159 cos (0.9 9^{\circ} (x - 18 2^{\circ})) = - 81

以下で両辺を割る

159

\frac{159 cos ( 0.9 9 ^{\circ} ( x - 18 2 ^{\circ} ) )}{159} = \frac{- 81}{159}

簡素化

\frac{159 cos ( 0.9 9 ^{\circ} ( x - 18 2 ^{\circ} ) )}{159} = \frac{- 81}{159}

簡素化

\frac{159 cos ( 0.9 9 ^{\circ} ( x - 18 2 ^{\circ} ) )}{159} : cos (0.9 9^{\circ} (x - 18 2^{\circ}))

\frac{159 cos ( 0.9 9 ^{\circ} ( x - 18 2 ^{\circ} ) )}{159}

数を割る:

\frac{159}{159} = 1

= cos (0.9 9^{\circ} (x - 18 2^{\circ}))

簡素化

\frac{- 81}{159} : - \frac{27}{53}

\frac{- 81}{159}

分数の規則を適用する:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{81}{159}

共通因数を約分する:

3

= - \frac{27}{53}

cos (0.9 9^{\circ} (x - 18 2^{\circ})) = - \frac{27}{53}

cos (0.9 9^{\circ} (x - 18 2^{\circ})) = - \frac{27}{53}

cos (0.9 9^{\circ} (x - 18 2^{\circ})) = - \frac{27}{53}

三角関数の逆数プロパティを適用する

cos (0.9 9^{\circ} (x - 18 2^{\circ})) = - \frac{27}{53}

以下の一般解

cos (0.9 9^{\circ} (x - 18 2^{\circ})) = - \frac{27}{53}

cos (x) = - a \Rightarrow x = arccos (- a) + 36 0^{\circ} n, x = - arccos (- a) + 36 0^{\circ} n

0.9 9^{\circ} (x - 18 2^{\circ}) = arccos (- \frac{27}{53}) + 36 0^{\circ} n, 0.9 9^{\circ} (x - 18 2^{\circ}) = - arccos (- \frac{27}{53}) + 36 0^{\circ} n

0.9 9^{\circ} (x - 18 2^{\circ}) = arccos (- \frac{27}{53}) + 36 0^{\circ} n, 0.9 9^{\circ} (x - 18 2^{\circ}) = - arccos (- \frac{27}{53}) + 36 0^{\circ} n

解く

0.9 9^{\circ} (x - 18 2^{\circ}) = arccos (- \frac{27}{53}) + 36 0^{\circ} n : x = 18 2^{\circ} + \frac{4000 n}{11} + \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}}

0.9 9^{\circ} (x - 18 2^{\circ}) = arccos (- \frac{27}{53}) + 36 0^{\circ} n

以下で両辺を乗じる:

2000

0.9 9^{\circ} (x - 18 2^{\circ}) = arccos (- \frac{27}{53}) + 36 0^{\circ} n

以下で両辺を乗じる:

2000

2000 \cdot 0.9 9^{\circ} (x - 18 2^{\circ}) = 2000 arccos (- \frac{27}{53}) + 2000 \cdot 36 0^{\circ} n

簡素化

2000 \cdot 0.9 9^{\circ} (x - 18 2^{\circ}) = 2000 arccos (- \frac{27}{53}) + 2000 \cdot 36 0^{\circ} n

簡素化

2000 \cdot 0.9 9^{\circ} (x - 18 2^{\circ}) : 198 0^{\circ} (x - 18 2^{\circ})

2000 \cdot 0.9 9^{\circ} (x - 18 2^{\circ})

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{11 \cdot 36000 0 ^{\circ}}{2000} (x - 18 2^{\circ})

共通因数を約分する:

2000

= (x - 18 2^{\circ}) \cdot 198 0^{\circ}

簡素化

2000 arccos (- \frac{27}{53}) + 2000 \cdot 36 0^{\circ} n : 2000 arccos (- \frac{27}{53}) + 72000 0^{\circ} n

2000 arccos (- \frac{27}{53}) + 2000 \cdot 36 0^{\circ} n

数を乗じる:

2000 \cdot 2 = 4000

= 2000 arccos (- \frac{27}{53}) + 72000 0^{\circ} n

198 0^{\circ} (x - 18 2^{\circ}) = 2000 arccos (- \frac{27}{53}) + 72000 0^{\circ} n

198 0^{\circ} (x - 18 2^{\circ}) = 2000 arccos (- \frac{27}{53}) + 72000 0^{\circ} n

198 0^{\circ} (x - 18 2^{\circ}) = 2000 arccos (- \frac{27}{53}) + 72000 0^{\circ} n

以下で両辺を割る

198 0^{\circ}

198 0^{\circ} (x - 18 2^{\circ}) = 2000 arccos (- \frac{27}{53}) + 72000 0^{\circ} n

以下で両辺を割る

198 0^{\circ}

\frac{198 0 ^{\circ} ( x - 18 2 ^{\circ} )}{198 0 ^{\circ}} = \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}} + \frac{72000 0 ^{\circ} n}{198 0 ^{\circ}}

簡素化

x - 18 2^{\circ} = \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}} + \frac{4000 n}{11}

x - 18 2^{\circ} = \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}} + \frac{4000 n}{11}

18 2^{\circ}

を右側に移動します

x - 18 2^{\circ} = \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}} + \frac{4000 n}{11}

両辺に

18 2^{\circ}

を足す

x - 18 2^{\circ} + 18 2^{\circ} = \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}} + \frac{4000 n}{11} + 18 2^{\circ}

簡素化

x - 18 2^{\circ} + 18 2^{\circ} = \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}} + \frac{4000 n}{11} + 18 2^{\circ}

簡素化

x - 18 2^{\circ} + 18 2^{\circ} : x

x - 18 2^{\circ} + 18 2^{\circ}

類似した元を足す:

- 18 2^{\circ} + 18 2^{\circ} = 0

= x

簡素化

\frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}} + \frac{4000 n}{11} + 18 2^{\circ} : 18 2^{\circ} + \frac{4000 n}{11} + \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}}

\frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}} + \frac{4000 n}{11} + 18 2^{\circ}

条件のようなグループ

= 18 2^{\circ} + \frac{4000 n}{11} + \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}}

さらに簡約できない

= 18 2^{\circ} + \frac{4000 n}{11} + \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}}

x = 18 2^{\circ} + \frac{4000 n}{11} + \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}}

x = 18 2^{\circ} + \frac{4000 n}{11} + \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}}

x = 18 2^{\circ} + \frac{4000 n}{11} + \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}}

解く

0.9 9^{\circ} (x - 18 2^{\circ}) = - arccos (- \frac{27}{53}) + 36 0^{\circ} n : x = 18 2^{\circ} + \frac{4000 n}{11} - \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}}

0.9 9^{\circ} (x - 18 2^{\circ}) = - arccos (- \frac{27}{53}) + 36 0^{\circ} n

以下で両辺を乗じる:

2000

0.9 9^{\circ} (x - 18 2^{\circ}) = - arccos (- \frac{27}{53}) + 36 0^{\circ} n

以下で両辺を乗じる:

2000

2000 \cdot 0.9 9^{\circ} (x - 18 2^{\circ}) = - 2000 arccos (- \frac{27}{53}) + 2000 \cdot 36 0^{\circ} n

簡素化

2000 \cdot 0.9 9^{\circ} (x - 18 2^{\circ}) = - 2000 arccos (- \frac{27}{53}) + 2000 \cdot 36 0^{\circ} n

簡素化

2000 \cdot 0.9 9^{\circ} (x - 18 2^{\circ}) : 198 0^{\circ} (x - 18 2^{\circ})

2000 \cdot 0.9 9^{\circ} (x - 18 2^{\circ})

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{11 \cdot 36000 0 ^{\circ}}{2000} (x - 18 2^{\circ})

共通因数を約分する:

2000

= (x - 18 2^{\circ}) \cdot 198 0^{\circ}

簡素化

- 2000 arccos (- \frac{27}{53}) + 2000 \cdot 36 0^{\circ} n : - 2000 arccos (- \frac{27}{53}) + 72000 0^{\circ} n

- 2000 arccos (- \frac{27}{53}) + 2000 \cdot 36 0^{\circ} n

数を乗じる:

2000 \cdot 2 = 4000

= - 2000 arccos (- \frac{27}{53}) + 72000 0^{\circ} n

198 0^{\circ} (x - 18 2^{\circ}) = - 2000 arccos (- \frac{27}{53}) + 72000 0^{\circ} n

198 0^{\circ} (x - 18 2^{\circ}) = - 2000 arccos (- \frac{27}{53}) + 72000 0^{\circ} n

198 0^{\circ} (x - 18 2^{\circ}) = - 2000 arccos (- \frac{27}{53}) + 72000 0^{\circ} n

以下で両辺を割る

198 0^{\circ}

198 0^{\circ} (x - 18 2^{\circ}) = - 2000 arccos (- \frac{27}{53}) + 72000 0^{\circ} n

以下で両辺を割る

198 0^{\circ}

\frac{198 0 ^{\circ} ( x - 18 2 ^{\circ} )}{198 0 ^{\circ}} = - \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}} + \frac{72000 0 ^{\circ} n}{198 0 ^{\circ}}

簡素化

x - 18 2^{\circ} = - \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}} + \frac{4000 n}{11}

x - 18 2^{\circ} = - \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}} + \frac{4000 n}{11}

18 2^{\circ}

を右側に移動します

x - 18 2^{\circ} = - \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}} + \frac{4000 n}{11}

両辺に

18 2^{\circ}

を足す

x - 18 2^{\circ} + 18 2^{\circ} = - \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}} + \frac{4000 n}{11} + 18 2^{\circ}

簡素化

x - 18 2^{\circ} + 18 2^{\circ} = - \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}} + \frac{4000 n}{11} + 18 2^{\circ}

簡素化

x - 18 2^{\circ} + 18 2^{\circ} : x

x - 18 2^{\circ} + 18 2^{\circ}

類似した元を足す:

- 18 2^{\circ} + 18 2^{\circ} = 0

= x

簡素化

- \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}} + \frac{4000 n}{11} + 18 2^{\circ} : 18 2^{\circ} + \frac{4000 n}{11} - \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}}

- \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}} + \frac{4000 n}{11} + 18 2^{\circ}

条件のようなグループ

= 18 2^{\circ} + \frac{4000 n}{11} - \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}}

さらに簡約できない

= 18 2^{\circ} + \frac{4000 n}{11} - \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}}

x = 18 2^{\circ} + \frac{4000 n}{11} - \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}}

x = 18 2^{\circ} + \frac{4000 n}{11} - \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}}

x = 18 2^{\circ} + \frac{4000 n}{11} - \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}}

x = 18 2^{\circ} + \frac{4000 n}{11} + \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}}, x = 18 2^{\circ} + \frac{4000 n}{11} - \frac{2000 arccos ( - \frac{27}{53} )}{198 0 ^{\circ}}

10進法形式で解を証明する

x = 18 2^{\circ} + \frac{4000 n}{11} + \frac{2000 \cdot 2.10532 \dots}{198 0 ^{\circ}}, x = 18 2^{\circ} + \frac{4000 n}{11} - \frac{2000 \cdot 2.10532 \dots}{198 0 ^{\circ}}

グラフ

人気の例

6cos(3x)=6cos(x)

6 cos (3 x) = 6 cos (x)

4cos(x)=-2sqrt(2)

4 cos (x) = - 22

tan(θ)=(0.15)/(0.5)

tan (θ) = \frac{0.15}{0.5}

arctan(x/(12))-arctan(x)=0.001

arctan (\frac{x}{12}) - arctan (x) = 0.001

2 = 2 cos (π + x)