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人気のある >

2cos(9x)=2-2cos(9x)

解

2 cos (9 x) = 2 - 2 cos (9 x)

解

x = \frac{π}{27} + \frac{2 πn}{9}, x = \frac{5 π}{27} + \frac{2 πn}{9}

+1

度

x = 6.66666 \dots^{\circ} + 4 0^{\circ} n, x = 33.33333 \dots^{\circ} + 4 0^{\circ} n

解答ステップ

2 cos (9 x) = 2 - 2 cos (9 x)

置換で解く

2 cos (9 x) = 2 - 2 cos (9 x)

仮定:

cos (9 x) = u

2 u = 2 - 2 u

2 u = 2 - 2 u : u = \frac{1}{2}

2 u = 2 - 2 u

2 u

を左側に移動します

2 u = 2 - 2 u

両辺に

2 u

を足す

2 u + 2 u = 2 - 2 u + 2 u

簡素化

4 u = 2

4 u = 2

以下で両辺を割る

4

4 u = 2

以下で両辺を割る

4

\frac{4 u}{4} = \frac{2}{4}

簡素化

u = \frac{1}{2}

u = \frac{1}{2}

代用を戻す

u = cos (9 x)

cos (9 x) = \frac{1}{2}

cos (9 x) = \frac{1}{2}

cos (9 x) = \frac{1}{2} : x = \frac{π}{27} + \frac{2 πn}{9}, x = \frac{5 π}{27} + \frac{2 πn}{9}

cos (9 x) = \frac{1}{2}

以下の一般解

cos (9 x) = \frac{1}{2}

cos (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} 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}

9 x = \frac{π}{3} + 2 πn, 9 x = \frac{5 π}{3} + 2 πn

9 x = \frac{π}{3} + 2 πn, 9 x = \frac{5 π}{3} + 2 πn

解く

9 x = \frac{π}{3} + 2 πn : x = \frac{π}{27} + \frac{2 πn}{9}

9 x = \frac{π}{3} + 2 πn

以下で両辺を割る

9

9 x = \frac{π}{3} + 2 πn

以下で両辺を割る

9

\frac{9 x}{9} = \frac{\frac{π}{3}}{9} + \frac{2 πn}{9}

簡素化

\frac{9 x}{9} = \frac{\frac{π}{3}}{9} + \frac{2 πn}{9}

簡素化

\frac{9 x}{9} : x

\frac{9 x}{9}

数を割る:

\frac{9}{9} = 1

= x

簡素化

\frac{\frac{π}{3}}{9} + \frac{2 πn}{9} : \frac{π}{27} + \frac{2 πn}{9}

\frac{\frac{π}{3}}{9} + \frac{2 πn}{9}

\frac{\frac{π}{3}}{9} = \frac{π}{27}

\frac{\frac{π}{3}}{9}

分数の規則を適用する:

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

= \frac{π}{3 \cdot 9}

数を乗じる:

3 \cdot 9 = 27

= \frac{π}{27}

= \frac{π}{27} + \frac{2 πn}{9}

x = \frac{π}{27} + \frac{2 πn}{9}

x = \frac{π}{27} + \frac{2 πn}{9}

x = \frac{π}{27} + \frac{2 πn}{9}

解く

9 x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{27} + \frac{2 πn}{9}

9 x = \frac{5 π}{3} + 2 πn

以下で両辺を割る

9

9 x = \frac{5 π}{3} + 2 πn

以下で両辺を割る

9

\frac{9 x}{9} = \frac{\frac{5 π}{3}}{9} + \frac{2 πn}{9}

簡素化

\frac{9 x}{9} = \frac{\frac{5 π}{3}}{9} + \frac{2 πn}{9}

簡素化

\frac{9 x}{9} : x

\frac{9 x}{9}

数を割る:

\frac{9}{9} = 1

= x

簡素化

\frac{\frac{5 π}{3}}{9} + \frac{2 πn}{9} : \frac{5 π}{27} + \frac{2 πn}{9}

\frac{\frac{5 π}{3}}{9} + \frac{2 πn}{9}

\frac{\frac{5 π}{3}}{9} = \frac{5 π}{27}

\frac{\frac{5 π}{3}}{9}

分数の規則を適用する:

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

= \frac{5 π}{3 \cdot 9}

数を乗じる:

3 \cdot 9 = 27

= \frac{5 π}{27}

= \frac{5 π}{27} + \frac{2 πn}{9}

x = \frac{5 π}{27} + \frac{2 πn}{9}

x = \frac{5 π}{27} + \frac{2 πn}{9}

x = \frac{5 π}{27} + \frac{2 πn}{9}

x = \frac{π}{27} + \frac{2 πn}{9}, x = \frac{5 π}{27} + \frac{2 πn}{9}

すべての解を組み合わせる

x = \frac{π}{27} + \frac{2 πn}{9}, x = \frac{5 π}{27} + \frac{2 πn}{9}

人気の例

sin(2x)=3sqrt(2),-pi<= x<= pi

sin (2 x) = 32, - π \leq x \leq π

5 cos^{2} (x) - 2 = 0

cos^2(x)+sec^2(x)=11

cos^{2} (x) + sec^{2} (x) = 11

5 cos^{2} (x) - 3 = 0

csc (2 x + 3^{\circ}) = \frac{5}{4}