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人気のある三角関数 >

sin(2x-pi/6)=0,0<= x<= 360

解

sin (2 x - \frac{π}{6}) = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

解

x = 1 5^{\circ}, x = 10 5^{\circ}, x = 19 5^{\circ}, x = 28 5^{\circ}

+1

ラジアン

x = \frac{π}{12}, x = \frac{7 π}{12}, x = \frac{13 π}{12}, x = \frac{19 π}{12}

解答ステップ

sin (2 x - \frac{π}{6}) = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

以下の一般解

sin (2 x - 3 0^{\circ}) = 0

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}

2 x - 3 0^{\circ} = 0 + 36 0^{\circ} n, 2 x - 3 0^{\circ} = 18 0^{\circ} + 36 0^{\circ} n

2 x - 3 0^{\circ} = 0 + 36 0^{\circ} n, 2 x - 3 0^{\circ} = 18 0^{\circ} + 36 0^{\circ} n

解く

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

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

0 + 36 0^{\circ} n = 36 0^{\circ} n

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

3 0^{\circ}

を右側に移動します

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

両辺に

3 0^{\circ}

を足す

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

簡素化

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

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

以下で両辺を割る

2

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

以下で両辺を割る

2

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

簡素化

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

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

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

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

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

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

解く

2 x - 3 0^{\circ} = 18 0^{\circ} + 36 0^{\circ} n : x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ}

2 x - 3 0^{\circ} = 18 0^{\circ} + 36 0^{\circ} n

3 0^{\circ}

を右側に移動します

2 x - 3 0^{\circ} = 18 0^{\circ} + 36 0^{\circ} n

両辺に

3 0^{\circ}

を足す

2 x - 3 0^{\circ} + 3 0^{\circ} = 18 0^{\circ} + 36 0^{\circ} n + 3 0^{\circ}

簡素化

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

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

以下で両辺を割る

2

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

以下で両辺を割る

2

\frac{2 x}{2} = 9 0^{\circ} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

簡素化

\frac{2 x}{2} = 9 0^{\circ} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\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{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2} : 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ}

9 0^{\circ} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{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 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}

= 9 0^{\circ} + 18 0^{\circ} n + 1 5^{\circ}

条件のようなグループ

= 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ}

x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ}

x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ}

x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ}

x = 18 0^{\circ} n + 1 5^{\circ}, x = 18 0^{\circ} n + 9 0^{\circ} + 1 5^{\circ}

範囲の解答

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

x = 1 5^{\circ}, x = 10 5^{\circ}, x = 19 5^{\circ}, x = 28 5^{\circ}

グラフ

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