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人気のある三角関数 >

sin(x/2)=-1/2

解

sin (\frac{x}{2}) = - \frac{1}{2}

解

x = \frac{7 π}{3} + 4 πn, x = \frac{11 π}{3} + 4 πn

+1

度

x = 42 0^{\circ} + 72 0^{\circ} n, x = 66 0^{\circ} + 72 0^{\circ} n

解答ステップ

sin (\frac{x}{2}) = - \frac{1}{2}

以下の一般解

sin (\frac{x}{2}) = - \frac{1}{2}

sin (x)

2 πn

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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

\frac{x}{2} = \frac{7 π}{6} + 2 πn, \frac{x}{2} = \frac{11 π}{6} + 2 πn

\frac{x}{2} = \frac{7 π}{6} + 2 πn, \frac{x}{2} = \frac{11 π}{6} + 2 πn

解く

\frac{x}{2} = \frac{7 π}{6} + 2 πn : x = \frac{7 π}{3} + 4 πn

\frac{x}{2} = \frac{7 π}{6} + 2 πn

以下で両辺を乗じる:

2

\frac{x}{2} = \frac{7 π}{6} + 2 πn

以下で両辺を乗じる:

2

\frac{2 x}{2} = 2 \cdot \frac{7 π}{6} + 2 \cdot 2 πn

簡素化

\frac{2 x}{2} = 2 \cdot \frac{7 π}{6} + 2 \cdot 2 πn

簡素化

\frac{2 x}{2} : x

\frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= x

簡素化

2 \cdot \frac{7 π}{6} + 2 \cdot 2 πn : \frac{7 π}{3} + 4 πn

2 \cdot \frac{7 π}{6} + 2 \cdot 2 πn

2 \cdot \frac{7 π}{6} = \frac{7 π}{3}

2 \cdot \frac{7 π}{6}

分数を乗じる:

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

= \frac{7 π 2}{6}

数を乗じる:

7 \cdot 2 = 14

= \frac{14 π}{6}

共通因数を約分する:

2

= \frac{7 π}{3}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

数を乗じる:

2 \cdot 2 = 4

= 4 πn

= \frac{7 π}{3} + 4 πn

x = \frac{7 π}{3} + 4 πn

x = \frac{7 π}{3} + 4 πn

x = \frac{7 π}{3} + 4 πn

解く

\frac{x}{2} = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{3} + 4 πn

\frac{x}{2} = \frac{11 π}{6} + 2 πn

以下で両辺を乗じる:

2

\frac{x}{2} = \frac{11 π}{6} + 2 πn

以下で両辺を乗じる:

2

\frac{2 x}{2} = 2 \cdot \frac{11 π}{6} + 2 \cdot 2 πn

簡素化

\frac{2 x}{2} = 2 \cdot \frac{11 π}{6} + 2 \cdot 2 πn

簡素化

\frac{2 x}{2} : x

\frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= x

簡素化

2 \cdot \frac{11 π}{6} + 2 \cdot 2 πn : \frac{11 π}{3} + 4 πn

2 \cdot \frac{11 π}{6} + 2 \cdot 2 πn

2 \cdot \frac{11 π}{6} = \frac{11 π}{3}

2 \cdot \frac{11 π}{6}

分数を乗じる:

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

= \frac{11 π 2}{6}

数を乗じる:

11 \cdot 2 = 22

= \frac{22 π}{6}

共通因数を約分する:

2

= \frac{11 π}{3}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

数を乗じる:

2 \cdot 2 = 4

= 4 πn

= \frac{11 π}{3} + 4 πn

x = \frac{11 π}{3} + 4 πn

x = \frac{11 π}{3} + 4 πn

x = \frac{11 π}{3} + 4 πn

x = \frac{7 π}{3} + 4 πn, x = \frac{11 π}{3} + 4 πn

グラフ

人気の例

cot(x)+1=csc(x)

cot (x) + 1 = csc (x)

2cos^2(x)+4sin^2(x)=3

2 cos^{2} (x) + 4 sin^{2} (x) = 3

solvefor x,sin(x)=1

so l v e f or x, sin (x) = 1

4 sec (θ) + 5 = 0

csc (2 x) - 1 = 0