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人気のある三角関数 >

csc(2x)=2,x0<x<360

解

csc (2 x) = 2, x 0^{\circ} < x < 36 0^{\circ}

解

以下の解はない : x \in R

解答ステップ

csc (2 x) = 2, x \cdot 0^{\circ} < x < 36 0^{\circ}

以下の一般解

csc (2 x) = 2

csc (x)

36 0^{\circ} n

循環を含む周期性テーブル:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

2 x = 3 0^{\circ} + 36 0^{\circ} n, 2 x = 15 0^{\circ} + 36 0^{\circ} n

2 x = 3 0^{\circ} + 36 0^{\circ} n, 2 x = 15 0^{\circ} + 36 0^{\circ} n

解く

2 x = 3 0^{\circ} + 36 0^{\circ} n : x = 1 5^{\circ} + 18 0^{\circ} n

2 x = 3 0^{\circ} + 36 0^{\circ} n

以下で両辺を割る

2

2 x = 3 0^{\circ} + 36 0^{\circ} n

以下で両辺を割る

2

\frac{2 x}{2} = \frac{3 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2}

簡素化

\frac{2 x}{2} = \frac{3 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{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{3 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} : 1 5^{\circ} + 18 0^{\circ} n

\frac{3 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2}

\frac{3 0 ^{\circ}}{2} = 1 5^{\circ}

\frac{3 0 ^{\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}}{6 \cdot 2}

数を乗じる:

6 \cdot 2 = 12

= 1 5^{\circ}

\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

= 1 5^{\circ} + 18 0^{\circ} n

x = 1 5^{\circ} + 18 0^{\circ} n

x = 1 5^{\circ} + 18 0^{\circ} n

x = 1 5^{\circ} + 18 0^{\circ} n

解く

2 x = 15 0^{\circ} + 36 0^{\circ} n : x = 7 5^{\circ} + 18 0^{\circ} n

2 x = 15 0^{\circ} + 36 0^{\circ} n

以下で両辺を割る

2

2 x = 15 0^{\circ} + 36 0^{\circ} n

以下で両辺を割る

2

\frac{2 x}{2} = \frac{15 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2}

簡素化

\frac{2 x}{2} = \frac{15 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{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{15 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} : 7 5^{\circ} + 18 0^{\circ} n

\frac{15 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2}

\frac{15 0 ^{\circ}}{2} = 7 5^{\circ}

\frac{15 0 ^{\circ}}{2}

分数の規則を適用する:

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

= \frac{90 0 ^{\circ}}{6 \cdot 2}

数を乗じる:

6 \cdot 2 = 12

= 7 5^{\circ}

\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

= 7 5^{\circ} + 18 0^{\circ} n

x = 7 5^{\circ} + 18 0^{\circ} n

x = 7 5^{\circ} + 18 0^{\circ} n

x = 7 5^{\circ} + 18 0^{\circ} n

x = 1 5^{\circ} + 18 0^{\circ} n, x = 7 5^{\circ} + 18 0^{\circ} n

範囲の解答

x 0 < x < 36 0^{\circ}

以下の解はない : x \in R

グラフ

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