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人気のある三角関数 >

csc^2(2x-0.6)=16

解

csc^{2} (2 x - 0.6) = 16

解

x = πn + \frac{0.6}{2} + \frac{0.25268 \dots}{2}, x = πn + \frac{π}{2} + \frac{0.6}{2} - \frac{0.25268 \dots}{2}, x = πn + \frac{0.6}{2} - \frac{0.25268 \dots}{2}, x = πn + \frac{π}{2} + \frac{0.6}{2} + \frac{0.25268 \dots}{2}

+1

度

x = 24.42748 \dots^{\circ} + 18 0^{\circ} n, x = 99.94997 \dots^{\circ} + 18 0^{\circ} n, x = 9.94997 \dots^{\circ} + 18 0^{\circ} n, x = 114.42748 \dots^{\circ} + 18 0^{\circ} n

解答ステップ

csc^{2} (2 x - 0.6) = 16

置換で解く

csc^{2} (2 x - 0.6) = 16

仮定:

csc (2 x - 0.6) = u

u^{2} = 16

u^{2} = 16 : u = 4, u = - 4

u^{2} = 16

x^{2} = f (a)

の場合, 解は

x = f (a), - f (a)

u = 16, u = - 16

16 = 4

16

数を因数に分解する:

16 = 4^{2}

= 4^{2}

累乗根の規則を適用する:

n a^{n} = a

4^{2} = 4

= 4

- 16 = - 4

- 16

16 = 4

16

数を因数に分解する:

16 = 4^{2}

= 4^{2}

累乗根の規則を適用する:

n a^{n} = a

4^{2} = 4

= 4

= - 4

u = 4, u = - 4

代用を戻す

u = csc (2 x - 0.6)

csc (2 x - 0.6) = 4, csc (2 x - 0.6) = - 4

csc (2 x - 0.6) = 4, csc (2 x - 0.6) = - 4

csc (2 x - 0.6) = 4 : x = πn + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}, x = πn + \frac{π}{2} + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

csc (2 x - 0.6) = 4

三角関数の逆数プロパティを適用する

csc (2 x - 0.6) = 4

以下の一般解

csc (2 x - 0.6) = 4

csc (x) = a \Rightarrow x = arccsc (a) + 2 πn, x = π - arccsc (a) + 2 πn

2 x - 0.6 = arccsc (4) + 2 πn, 2 x - 0.6 = π - arccsc (4) + 2 πn

2 x - 0.6 = arccsc (4) + 2 πn, 2 x - 0.6 = π - arccsc (4) + 2 πn

解く

2 x - 0.6 = arccsc (4) + 2 πn : x = πn + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

2 x - 0.6 = arccsc (4) + 2 πn

0.6

を右側に移動します

2 x - 0.6 = arccsc (4) + 2 πn

両辺に

0.6

を足す

2 x - 0.6 + 0.6 = arccsc (4) + 2 πn + 0.6

簡素化

2 x = arccsc (4) + 2 πn + 0.6

2 x = arccsc (4) + 2 πn + 0.6

以下で両辺を割る

2

2 x = arccsc (4) + 2 πn + 0.6

以下で両辺を割る

2

\frac{2 x}{2} = \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2}

簡素化

\frac{2 x}{2} = \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{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{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2} : πn + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

\frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2}

条件のようなグループ

= \frac{0.6}{2} + \frac{2 πn}{2} + \frac{arccsc ( 4 )}{2}

数を割る:

\frac{2}{2} = 1

= \frac{0.6}{2} + πn + \frac{arccsc ( 4 )}{2}

条件のようなグループ

= πn + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

x = πn + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

x = πn + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

x = πn + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

解く

2 x - 0.6 = π - arccsc (4) + 2 πn : x = πn + \frac{π}{2} + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

2 x - 0.6 = π - arccsc (4) + 2 πn

0.6

を右側に移動します

2 x - 0.6 = π - arccsc (4) + 2 πn

両辺に

0.6

を足す

2 x - 0.6 + 0.6 = π - arccsc (4) + 2 πn + 0.6

簡素化

2 x = π - arccsc (4) + 2 πn + 0.6

2 x = π - arccsc (4) + 2 πn + 0.6

以下で両辺を割る

2

2 x = π - arccsc (4) + 2 πn + 0.6

以下で両辺を割る

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2}

簡素化

\frac{2 x}{2} = \frac{π}{2} - \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{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{π}{2} - \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2} : πn + \frac{π}{2} + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

\frac{π}{2} - \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2}

条件のようなグループ

= \frac{π}{2} + \frac{0.6}{2} + \frac{2 πn}{2} - \frac{arccsc ( 4 )}{2}

数を割る:

\frac{2}{2} = 1

= \frac{π}{2} + \frac{0.6}{2} + πn - \frac{arccsc ( 4 )}{2}

条件のようなグループ

= πn + \frac{π}{2} + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

x = πn + \frac{π}{2} + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

x = πn + \frac{π}{2} + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

x = πn + \frac{π}{2} + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

x = πn + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}, x = πn + \frac{π}{2} + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

csc (2 x - 0.6) = - 4 : x = πn + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}, x = πn + \frac{π}{2} + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

csc (2 x - 0.6) = - 4

三角関数の逆数プロパティを適用する

csc (2 x - 0.6) = - 4

以下の一般解

csc (2 x - 0.6) = - 4

csc (x) = - a \Rightarrow x = arccsc (- a) + 2 πn, x = π + arccsc (a) + 2 πn

2 x - 0.6 = arccsc (- 4) + 2 πn, 2 x - 0.6 = π + arccsc (4) + 2 πn

2 x - 0.6 = arccsc (- 4) + 2 πn, 2 x - 0.6 = π + arccsc (4) + 2 πn

解く

2 x - 0.6 = arccsc (- 4) + 2 πn : x = πn + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

2 x - 0.6 = arccsc (- 4) + 2 πn

簡素化

arccsc (- 4) + 2 πn : - arccsc (4) + 2 πn

arccsc (- 4) + 2 πn

次のプロパティを使用する:

arccsc (- x) = - arccsc (x)

arccsc (- 4) = - arccsc (4)

= - arccsc (4) + 2 πn

2 x - 0.6 = - arccsc (4) + 2 πn

0.6

を右側に移動します

2 x - 0.6 = - arccsc (4) + 2 πn

両辺に

0.6

を足す

2 x - 0.6 + 0.6 = - arccsc (4) + 2 πn + 0.6

簡素化

2 x = - arccsc (4) + 2 πn + 0.6

2 x = - arccsc (4) + 2 πn + 0.6

以下で両辺を割る

2

2 x = - arccsc (4) + 2 πn + 0.6

以下で両辺を割る

2

\frac{2 x}{2} = - \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2}

簡素化

\frac{2 x}{2} = - \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{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{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2} : πn + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

- \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2}

条件のようなグループ

= \frac{0.6}{2} + \frac{2 πn}{2} - \frac{arccsc ( 4 )}{2}

数を割る:

\frac{2}{2} = 1

= \frac{0.6}{2} + πn - \frac{arccsc ( 4 )}{2}

条件のようなグループ

= πn + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

x = πn + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

x = πn + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

x = πn + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}

解く

2 x - 0.6 = π + arccsc (4) + 2 πn : x = πn + \frac{π}{2} + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

2 x - 0.6 = π + arccsc (4) + 2 πn

0.6

を右側に移動します

2 x - 0.6 = π + arccsc (4) + 2 πn

両辺に

0.6

を足す

2 x - 0.6 + 0.6 = π + arccsc (4) + 2 πn + 0.6

簡素化

2 x = π + arccsc (4) + 2 πn + 0.6

2 x = π + arccsc (4) + 2 πn + 0.6

以下で両辺を割る

2

2 x = π + arccsc (4) + 2 πn + 0.6

以下で両辺を割る

2

\frac{2 x}{2} = \frac{π}{2} + \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2}

簡素化

\frac{2 x}{2} = \frac{π}{2} + \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{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{π}{2} + \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2} : πn + \frac{π}{2} + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

\frac{π}{2} + \frac{arccsc ( 4 )}{2} + \frac{2 πn}{2} + \frac{0.6}{2}

条件のようなグループ

= \frac{π}{2} + \frac{0.6}{2} + \frac{2 πn}{2} + \frac{arccsc ( 4 )}{2}

数を割る:

\frac{2}{2} = 1

= \frac{π}{2} + \frac{0.6}{2} + πn + \frac{arccsc ( 4 )}{2}

条件のようなグループ

= πn + \frac{π}{2} + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

x = πn + \frac{π}{2} + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

x = πn + \frac{π}{2} + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

x = πn + \frac{π}{2} + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

x = πn + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}, x = πn + \frac{π}{2} + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

すべての解を組み合わせる

x = πn + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}, x = πn + \frac{π}{2} + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}, x = πn + \frac{0.6}{2} - \frac{arccsc ( 4 )}{2}, x = πn + \frac{π}{2} + \frac{0.6}{2} + \frac{arccsc ( 4 )}{2}

10進法形式で解を証明する

x = πn + \frac{0.6}{2} + \frac{0.25268 \dots}{2}, x = πn + \frac{π}{2} + \frac{0.6}{2} - \frac{0.25268 \dots}{2}, x = πn + \frac{0.6}{2} - \frac{0.25268 \dots}{2}, x = πn + \frac{π}{2} + \frac{0.6}{2} + \frac{0.25268 \dots}{2}

グラフ

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