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人気のある三角関数 >

sin(5x)+sin(7x)=0,-90<= x<90

解

sin (5 x) + sin (7 x) = 0, - 9 0^{\circ} \leq x < 9 0^{\circ}

解

x = - 9 0^{\circ}, x = 0, x = 3 0^{\circ}, x = 6 0^{\circ}, x = - 6 0^{\circ}, x = - 3 0^{\circ}

+1

ラジアン

x = - \frac{π}{2}, x = 0, x = \frac{π}{6}, x = \frac{π}{3}, x = - \frac{π}{3}, x = - \frac{π}{6}

解答ステップ

sin (5 x) + sin (7 x) = 0, - 9 0^{\circ} \leq x < 9 0^{\circ}

三角関数の公式を使用して書き換える

sin (5 x) + sin (7 x)

和・積の公式を使用する:

sin (s) + sin (t) = 2 sin (\frac{s + t}{2}) cos (\frac{s - t}{2})

= 2 sin (\frac{5 x + 7 x}{2}) cos (\frac{5 x - 7 x}{2})

簡素化

2 sin (\frac{5 x + 7 x}{2}) cos (\frac{5 x - 7 x}{2}) : 2 cos (x) sin (6 x)

2 sin (\frac{5 x + 7 x}{2}) cos (\frac{5 x - 7 x}{2})

\frac{5 x + 7 x}{2} = 6 x

\frac{5 x + 7 x}{2}

類似した元を足す:

5 x + 7 x = 12 x

= \frac{12 x}{2}

数を割る:

\frac{12}{2} = 6

= 6 x

= 2 sin (6 x) cos (\frac{5 x - 7 x}{2})

\frac{5 x - 7 x}{2} = - x

\frac{5 x - 7 x}{2}

類似した元を足す:

5 x - 7 x = - 2 x

= \frac{- 2 x}{2}

分数の規則を適用する:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= - x

= 2 sin (6 x) cos (- x)

負角の公式を使用する:

cos (- x) = cos (x)

= 2 cos (x) sin (6 x)

= 2 cos (x) sin (6 x)

2 cos (x) sin (6 x) = 0

各部分を別個に解く

cos (x) = 0 or sin (6 x) = 0

cos (x) = 0, - 9 0^{\circ} \leq x < 9 0^{\circ} : x = - 9 0^{\circ}

cos (x) = 0, - 9 0^{\circ} \leq x < 9 0^{\circ}

以下の一般解

cos (x) = 0

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

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n

範囲の解答

- 9 0^{\circ} \leq x < 9 0^{\circ}

x = - 9 0^{\circ}

sin (6 x) = 0, - 9 0^{\circ} \leq x < 9 0^{\circ} : x = 0, x = 3 0^{\circ}, x = 6 0^{\circ}, x = - 6 0^{\circ}, x = - 3 0^{\circ}, x = - 9 0^{\circ}

sin (6 x) = 0, - 9 0^{\circ} \leq x < 9 0^{\circ}

以下の一般解

sin (6 x) = 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}

6 x = 0 + 36 0^{\circ} n, 6 x = 18 0^{\circ} + 36 0^{\circ} n

6 x = 0 + 36 0^{\circ} n, 6 x = 18 0^{\circ} + 36 0^{\circ} n

解く

6 x = 0 + 36 0^{\circ} n : x = \frac{18 0 ^{\circ} n}{3}

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

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

6 x = 36 0^{\circ} n

以下で両辺を割る

6

6 x = 36 0^{\circ} n

以下で両辺を割る

6

\frac{6 x}{6} = \frac{36 0 ^{\circ} n}{6}

簡素化

x = \frac{18 0 ^{\circ} n}{3}

x = \frac{18 0 ^{\circ} n}{3}

解く

6 x = 18 0^{\circ} + 36 0^{\circ} n : x = 3 0^{\circ} + \frac{18 0 ^{\circ} n}{3}

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

以下で両辺を割る

6

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

以下で両辺を割る

6

\frac{6 x}{6} = 3 0^{\circ} + \frac{36 0 ^{\circ} n}{6}

簡素化

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

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

x = \frac{18 0 ^{\circ} n}{3}, x = 3 0^{\circ} + \frac{18 0 ^{\circ} n}{3}

範囲の解答

- 9 0^{\circ} \leq x < 9 0^{\circ}

x = 0, x = 3 0^{\circ}, x = 6 0^{\circ}, x = - 6 0^{\circ}, x = - 3 0^{\circ}, x = - 9 0^{\circ}

すべての解を組み合わせる

x = - 9 0^{\circ}, x = 0, x = 3 0^{\circ}, x = 6 0^{\circ}, x = - 6 0^{\circ}, x = - 3 0^{\circ}

グラフ

人気の例

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arcsin(x)=(3pi)/7

arcsin (x) = \frac{3 π}{7}

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