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人気のある >

csc(2x+3)= 5/4

解

csc (2 x + 3^{\circ}) = \frac{5}{4}

解

x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{0.92729 \dots}{2}, x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{0.92729 \dots}{2}

+1

ラジアン

x = - \frac{π}{120} + \frac{0.92729 \dots}{2} + πn, x = \frac{π}{2} - \frac{π}{120} - \frac{0.92729 \dots}{2} + πn

解答ステップ

csc (2 x + 3^{\circ}) = \frac{5}{4}

三角関数の逆数プロパティを適用する

csc (2 x + 3^{\circ}) = \frac{5}{4}

以下の一般解

csc (2 x + 3^{\circ}) = \frac{5}{4}

csc (x) = a \Rightarrow x = arccsc (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arccsc (a) + 36 0^{\circ} n

2 x + 3^{\circ} = arccsc (\frac{5}{4}) + 36 0^{\circ} n, 2 x + 3^{\circ} = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n

2 x + 3^{\circ} = arccsc (\frac{5}{4}) + 36 0^{\circ} n, 2 x + 3^{\circ} = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n

解く

2 x + 3^{\circ} = arccsc (\frac{5}{4}) + 36 0^{\circ} n : x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}

2 x + 3^{\circ} = arccsc (\frac{5}{4}) + 36 0^{\circ} n

3^{\circ}

を右側に移動します

2 x + 3^{\circ} = arccsc (\frac{5}{4}) + 36 0^{\circ} n

両辺から

3^{\circ}

を引く

2 x + 3^{\circ} - 3^{\circ} = arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

簡素化

2 x = arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

2 x = arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

以下で両辺を割る

2

2 x = arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

以下で両辺を割る

2

\frac{2 x}{2} = \frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2}

簡素化

\frac{2 x}{2} = \frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{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 ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2} : 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}

\frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2}

条件のようなグループ

= \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2} + \frac{arccsc ( \frac{5}{4} )}{2}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

数を割る:

\frac{2}{2} = 1

= 18 0^{\circ} n

\frac{3 ^{\circ}}{2} = 1. 5^{\circ}

\frac{3 ^{\circ}}{2}

分数の規則を適用する:

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

= \frac{18 0 ^{\circ}}{60 \cdot 2}

数を乗じる:

60 \cdot 2 = 120

= 1. 5^{\circ}

= 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}

x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}

x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}

x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}

解く

2 x + 3^{\circ} = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n : x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

2 x + 3^{\circ} = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n

3^{\circ}

を右側に移動します

2 x + 3^{\circ} = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n

両辺から

3^{\circ}

を引く

2 x + 3^{\circ} - 3^{\circ} = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

簡素化

2 x = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

2 x = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

以下で両辺を割る

2

2 x = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

以下で両辺を割る

2

\frac{2 x}{2} = 9 0^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2}

簡素化

\frac{2 x}{2} = 9 0^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{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

9 0^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2} : 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

9 0^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2}

条件のようなグループ

= 9 0^{\circ} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2} - \frac{arccsc ( \frac{5}{4} )}{2}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

数を割る:

\frac{2}{2} = 1

= 18 0^{\circ} n

\frac{3 ^{\circ}}{2} = 1. 5^{\circ}

\frac{3 ^{\circ}}{2}

分数の規則を適用する:

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

= \frac{18 0 ^{\circ}}{60 \cdot 2}

数を乗じる:

60 \cdot 2 = 120

= 1. 5^{\circ}

= 9 0^{\circ} + 18 0^{\circ} n - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

条件のようなグループ

= 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}, x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

10進法形式で解を証明する

x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{0.92729 \dots}{2}, x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{0.92729 \dots}{2}

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