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人気のある三角関数 >

2sin(1/2 x)=1,0<= x<= 12

解

2 sin (\frac{1}{2} x) = 1, 0^{\circ} \leq x \leq 1 2^{\circ}

解

以下の解はない : x \in R

解答ステップ

2 sin (\frac{1}{2} x) = 1, 0^{\circ} \leq x \leq 1 2^{\circ}

以下で両辺を割る

2

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

以下で両辺を割る

2

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

簡素化

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

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

以下の一般解

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

sin (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} 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{1}{2} x = 3 0^{\circ} + 36 0^{\circ} n, \frac{1}{2} x = 15 0^{\circ} + 36 0^{\circ} n

\frac{1}{2} x = 3 0^{\circ} + 36 0^{\circ} n, \frac{1}{2} x = 15 0^{\circ} + 36 0^{\circ} n

解く

\frac{1}{2} x = 3 0^{\circ} + 36 0^{\circ} n : x = 6 0^{\circ} + 72 0^{\circ} n

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

以下で両辺を乗じる:

2

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

以下で両辺を乗じる:

2

2 \cdot \frac{1}{2} x = 2 \cdot 3 0^{\circ} + 2 \cdot 36 0^{\circ} n

簡素化

2 \cdot \frac{1}{2} x = 2 \cdot 3 0^{\circ} + 2 \cdot 36 0^{\circ} n

簡素化

2 \cdot \frac{1}{2} x : x

2 \cdot \frac{1}{2} x

分数を乗じる:

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

= \frac{1 \cdot 2}{2} x

共通因数を約分する:

2

= x \cdot 1

乗算:

x \cdot 1 = x

= x

簡素化

2 \cdot 3 0^{\circ} + 2 \cdot 36 0^{\circ} n : 6 0^{\circ} + 72 0^{\circ} n

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

2 \cdot 3 0^{\circ} = 6 0^{\circ}

2 \cdot 3 0^{\circ}

分数を乗じる:

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

= 6 0^{\circ}

共通因数を約分する:

2

= 6 0^{\circ}

2 \cdot 36 0^{\circ} n = 72 0^{\circ} n

2 \cdot 36 0^{\circ} n

数を乗じる:

2 \cdot 2 = 4

= 72 0^{\circ} n

= 6 0^{\circ} + 72 0^{\circ} n

x = 6 0^{\circ} + 72 0^{\circ} n

x = 6 0^{\circ} + 72 0^{\circ} n

x = 6 0^{\circ} + 72 0^{\circ} n

解く

\frac{1}{2} x = 15 0^{\circ} + 36 0^{\circ} n : x = 30 0^{\circ} + 72 0^{\circ} n

\frac{1}{2} x = 15 0^{\circ} + 36 0^{\circ} n

以下で両辺を乗じる:

2

\frac{1}{2} x = 15 0^{\circ} + 36 0^{\circ} n

以下で両辺を乗じる:

2

2 \cdot \frac{1}{2} x = 2 \cdot 15 0^{\circ} + 2 \cdot 36 0^{\circ} n

簡素化

2 \cdot \frac{1}{2} x = 2 \cdot 15 0^{\circ} + 2 \cdot 36 0^{\circ} n

簡素化

2 \cdot \frac{1}{2} x : x

2 \cdot \frac{1}{2} x

分数を乗じる:

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

= \frac{1 \cdot 2}{2} x

共通因数を約分する:

2

= x \cdot 1

乗算:

x \cdot 1 = x

= x

簡素化

2 \cdot 15 0^{\circ} + 2 \cdot 36 0^{\circ} n : 30 0^{\circ} + 72 0^{\circ} n

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

2 \cdot 15 0^{\circ} = 30 0^{\circ}

2 \cdot 15 0^{\circ}

分数を乗じる:

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

= 30 0^{\circ}

数を乗じる:

5 \cdot 2 = 10

= 30 0^{\circ}

共通因数を約分する:

2

= 30 0^{\circ}

2 \cdot 36 0^{\circ} n = 72 0^{\circ} n

2 \cdot 36 0^{\circ} n

数を乗じる:

2 \cdot 2 = 4

= 72 0^{\circ} n

= 30 0^{\circ} + 72 0^{\circ} n

x = 30 0^{\circ} + 72 0^{\circ} n

x = 30 0^{\circ} + 72 0^{\circ} n

x = 30 0^{\circ} + 72 0^{\circ} n

x = 6 0^{\circ} + 72 0^{\circ} n, x = 30 0^{\circ} + 72 0^{\circ} n

範囲の解答

0 \leq x \leq 1 2^{\circ}

以下の解はない : x \in R

グラフ

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